LMFDB - Embedded newform 588.2.o.e.31.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [588,2,Mod(19,588)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(588, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("588.19"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	588.o (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [24,-4,-12,4,0,8,0,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(8)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.69520363885$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.9
Character	$\chi$	$=$	588.31
Dual form			588.2.o.e.19.9

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.772298 - 1.18472i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.807113 - 1.82991i) q^{4} +(2.68862 - 1.55228i) q^{5} +(0.639847 + 1.26119i) q^{6} +(-2.79126 - 0.457034i) q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.237406 - 4.38407i) q^{10} +(-4.62852 - 2.67228i) q^{11} +(1.98830 + 0.215975i) q^{12} -3.92787i q^{13} +3.10455i q^{15} +(-2.69714 + 2.95389i) q^{16} +(4.92057 + 2.84089i) q^{17} +(-1.41214 - 0.0764704i) q^{18} +(-0.0854065 - 0.147928i) q^{19} +(-5.01054 - 3.66707i) q^{20} +(-6.74049 + 3.41969i) q^{22} +(5.31006 - 3.06576i) q^{23} +(1.79143 - 2.18878i) q^{24} +(2.31912 - 4.01683i) q^{25} +(-4.65342 - 3.03348i) q^{26} +1.00000 q^{27} -1.96817 q^{29} +(3.67802 + 2.39764i) q^{30} +(0.765577 - 1.32602i) q^{31} +(1.41653 + 5.47663i) q^{32} +(4.62852 - 2.67228i) q^{33} +(7.16580 - 3.63547i) q^{34} +(-1.18119 + 1.61393i) q^{36} +(-4.46997 - 7.74221i) q^{37} +(-0.241213 - 0.0130621i) q^{38} +(3.40163 + 1.96393i) q^{39} +(-8.21407 + 3.10401i) q^{40} +5.84308i q^{41} +2.38285i q^{43} +(-1.15429 + 10.6266i) q^{44} +(-2.68862 - 1.55228i) q^{45} +(0.468881 - 8.65860i) q^{46} +(-1.14739 - 1.98733i) q^{47} +(-1.20957 - 3.81273i) q^{48} +(-2.96776 - 5.84969i) q^{50} +(-4.92057 + 2.84089i) q^{51} +(-7.18765 + 3.17023i) q^{52} +(0.599523 - 1.03840i) q^{53} +(0.772298 - 1.18472i) q^{54} -16.5924 q^{55} +0.170813 q^{57} +(-1.52001 + 2.33172i) q^{58} +(-5.49711 + 9.52127i) q^{59} +(5.68105 - 2.50572i) q^{60} +(5.70691 - 3.29489i) q^{61} +(-0.979705 - 1.93107i) q^{62} +(7.58224 + 2.55140i) q^{64} +(-6.09713 - 10.5605i) q^{65} +(0.408700 - 7.54728i) q^{66} +(8.35536 + 4.82397i) q^{67} +(1.22712 - 11.2971i) q^{68} +6.13153i q^{69} +2.04649i q^{71} +(0.999826 + 2.64582i) q^{72} +(8.89617 + 5.13620i) q^{73} +(-12.6245 - 0.683641i) q^{74} +(2.31912 + 4.01683i) q^{75} +(-0.201763 + 0.275681i) q^{76} +(4.95378 - 2.51324i) q^{78} +(12.4661 - 7.19733i) q^{79} +(-2.66633 + 12.1286i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(6.92240 + 4.51259i) q^{82} +10.9783 q^{83} +17.6394 q^{85} +(2.82300 + 1.84027i) q^{86} +(0.984084 - 1.70448i) q^{87} +(11.6981 + 9.57440i) q^{88} +(-5.03915 + 2.90936i) q^{89} +(-3.91542 + 1.98644i) q^{90} +(-9.89588 - 7.24251i) q^{92} +(0.765577 + 1.32602i) q^{93} +(-3.24055 - 0.175482i) q^{94} +(-0.459251 - 0.265149i) q^{95} +(-5.45116 - 1.51156i) q^{96} -2.32666i q^{97} +5.34455i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{2} - 12 q^{3} + 4 q^{4} + 8 q^{6} + 8 q^{8} - 12 q^{9} + 4 q^{12} + 4 q^{16} - 4 q^{18} - 48 q^{20} - 4 q^{24} + 12 q^{25} - 24 q^{26} + 24 q^{27} + 64 q^{29} - 16 q^{31} - 4 q^{32} + 64 q^{34}+ \cdots - 4 q^{96}+O(q^{100}) $ 24 * q - 4 * q^2 - 12 * q^3 + 4 * q^4 + 8 * q^6 + 8 * q^8 - 12 * q^9 + 4 * q^12 + 4 * q^16 - 4 * q^18 - 48 * q^20 - 4 * q^24 + 12 * q^25 - 24 * q^26 + 24 * q^27 + 64 * q^29 - 16 * q^31 - 4 * q^32 + 64 * q^34 - 8 * q^36 - 32 * q^37 + 24 * q^38 + 32 * q^40 + 24 * q^44 - 24 * q^46 - 8 * q^48 - 56 * q^50 - 32 * q^52 + 32 * q^53 - 4 * q^54 + 32 * q^55 - 16 * q^58 + 16 * q^59 + 24 * q^60 + 16 * q^62 - 8 * q^64 + 8 * q^68 - 4 * q^72 + 32 * q^74 + 12 * q^75 - 64 * q^76 + 48 * q^78 + 16 * q^80 - 12 * q^81 - 32 * q^82 - 32 * q^83 + 32 * q^85 + 24 * q^86 - 32 * q^87 - 24 * q^88 - 16 * q^93 - 4 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.772298	−	1.18472i	0.546097	−	0.837722i
$2$	0.772298	−	1.18472i	0.546097	−	0.837722i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	−0.807113	−	1.82991i	−0.403556	−	0.914955i
$5$	2.68862	−	1.55228i	1.20239	−	0.694199i	0.241302	−	0.970450i	$-0.422426\pi$
$5$	2.68862	−	1.55228i	1.20239	−	0.694199i	0.961085	+	0.276251i	$0.0890923\pi$
$6$	0.639847	+	1.26119i	0.261216	+	0.514878i
$7$		0			0
$7$		0			0
$8$	−2.79126	−	0.457034i	−0.986859	−	0.161586i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	0.237406	−	4.38407i	0.0750745	−	1.38637i
$11$	−4.62852	−	2.67228i	−1.39555	−	0.805721i	−0.401628	−	0.915803i	$-0.631555\pi$
$11$	−4.62852	−	2.67228i	−1.39555	−	0.805721i	−0.993923	+	0.110082i	$0.964889\pi$
$12$	1.98830	+	0.215975i	0.573974	+	0.0623465i
$13$		−	3.92787i		−	1.08939i	−0.838633	−	0.544697i	$-0.816644\pi$
$13$		−	3.92787i		−	1.08939i	0.838633	−	0.544697i	$-0.183356\pi$
$14$		0			0
$15$			3.10455i			0.801592i
$16$	−2.69714	+	2.95389i	−0.674285	+	0.738472i
$17$	4.92057	+	2.84089i	1.19341	+	0.689017i	0.959079	−	0.283139i	$-0.0913758\pi$
$17$	4.92057	+	2.84089i	1.19341	+	0.689017i	0.234334	+	0.972156i	$0.424709\pi$
$18$	−1.41214	−	0.0764704i	−0.332846	−	0.0180243i
$19$	−0.0854065	−	0.147928i	−0.0195936	−	0.0339371i	0.856062	−	0.516873i	$-0.172904\pi$
$19$	−0.0854065	−	0.147928i	−0.0195936	−	0.0339371i	−0.875656	+	0.482935i	$0.839571\pi$
$20$	−5.01054	−	3.66707i	−1.12039	−	0.819982i
$21$		0			0
$22$	−6.74049	+	3.41969i	−1.43708	+	0.729081i
$23$	5.31006	−	3.06576i	1.10722	−	0.639256i	0.169115	−	0.985596i	$-0.445909\pi$
$23$	5.31006	−	3.06576i	1.10722	−	0.639256i	0.938109	+	0.346341i	$0.112576\pi$
$24$	1.79143	−	2.18878i	0.365675	−	0.446783i
$25$	2.31912	−	4.01683i	0.463824	−	0.803366i
$26$	−4.65342	−	3.03348i	−0.912610	−	0.594915i
$27$	1.00000			0.192450
$28$		0			0
$29$	−1.96817			−0.365480			−0.182740	−	0.983161i	$-0.558497\pi$
$29$	−1.96817			−0.365480			−0.182740	+	0.983161i	$0.558497\pi$
$30$	3.67802	+	2.39764i	0.671511	+	0.437747i
$31$	0.765577	−	1.32602i	0.137502	−	0.238160i	−0.789049	−	0.614331i	$-0.789426\pi$
$31$	0.765577	−	1.32602i	0.137502	−	0.238160i	0.926550	+	0.376171i	$0.122759\pi$
$32$	1.41653	+	5.47663i	0.250409	+	0.968140i
$33$	4.62852	−	2.67228i	0.805721	−	0.465183i
$34$	7.16580	−	3.63547i	1.22892	−	0.623478i
$35$		0			0
$36$	−1.18119	+	1.61393i	−0.196865	+	0.268989i
$37$	−4.46997	−	7.74221i	−0.734858	−	1.27281i	−0.954786	−	0.297295i	$-0.903915\pi$
$37$	−4.46997	−	7.74221i	−0.734858	−	1.27281i	0.219927	−	0.975516i	$-0.429418\pi$
$38$	−0.241213	−	0.0130621i	−0.0391299	−	0.00211896i
$39$	3.40163	+	1.96393i	0.544697	+	0.314481i
$40$	−8.21407	+	3.10401i	−1.29876	+	0.490787i
$41$			5.84308i			0.912535i	0.889843	+	0.456268i	$0.150814\pi$
$41$			5.84308i			0.912535i	−0.889843	+	0.456268i	$0.849186\pi$
$42$		0			0
$43$			2.38285i			0.363381i	0.983356	+	0.181691i	$0.0581569\pi$
$43$			2.38285i			0.363381i	−0.983356	+	0.181691i	$0.941843\pi$
$44$	−1.15429	+	10.6266i	−0.174015	+	1.60202i
$45$	−2.68862	−	1.55228i	−0.400796	−	0.231400i
$46$	0.468881	−	8.65860i	0.0691327	−	1.27664i
$47$	−1.14739	−	1.98733i	−0.167364	−	0.289882i	0.770128	−	0.637889i	$-0.220192\pi$
$47$	−1.14739	−	1.98733i	−0.167364	−	0.289882i	−0.937492	+	0.348006i	$0.886859\pi$
$48$	−1.20957	−	3.81273i	−0.174587	−	0.550321i
$49$		0			0
$50$	−2.96776	−	5.84969i	−0.419705	−	0.827271i
$51$	−4.92057	+	2.84089i	−0.689017	+	0.397804i
$52$	−7.18765	+	3.17023i	−0.996747	+	0.439632i
$53$	0.599523	−	1.03840i	0.0823508	−	0.142636i	−0.821908	−	0.569620i	$-0.807091\pi$
$53$	0.599523	−	1.03840i	0.0823508	−	0.142636i	0.904259	+	0.426984i	$0.140424\pi$
$54$	0.772298	−	1.18472i	0.105096	−	0.161220i
$55$	−16.5924			−2.23732
$56$		0			0
$57$	0.170813			0.0226247
$58$	−1.52001	+	2.33172i	−0.199587	+	0.306170i
$59$	−5.49711	+	9.52127i	−0.715663	+	1.23956i	0.247041	+	0.969005i	$0.420542\pi$
$59$	−5.49711	+	9.52127i	−0.715663	+	1.23956i	−0.962703	+	0.270559i	$0.912791\pi$
$60$	5.68105	−	2.50572i	0.733420	−	0.323487i
$61$	5.70691	−	3.29489i	0.730695	−	0.421867i	−0.0879813	−	0.996122i	$-0.528042\pi$
$61$	5.70691	−	3.29489i	0.730695	−	0.421867i	0.818676	+	0.574255i	$0.194708\pi$
$62$	−0.979705	−	1.93107i	−0.124423	−	0.245247i
$63$		0			0
$64$	7.58224	+	2.55140i	0.947780	+	0.318925i
$65$	−6.09713	−	10.5605i	−0.756257	−	1.30987i
$66$	0.408700	−	7.54728i	0.0503075	−	0.929006i
$67$	8.35536	+	4.82397i	1.02077	+	0.589342i	0.914327	−	0.404977i	$-0.132720\pi$
$67$	8.35536	+	4.82397i	1.02077	+	0.589342i	0.106443	+	0.994319i	$0.466054\pi$
$68$	1.22712	−	11.2971i	0.148810	−	1.36998i
$69$			6.13153i			0.738149i
$70$		0			0
$71$			2.04649i			0.242873i	0.992599	+	0.121437i	$0.0387501\pi$
$71$			2.04649i			0.242873i	−0.992599	+	0.121437i	$0.961250\pi$
$72$	0.999826	+	2.64582i	0.117831	+	0.311813i
$73$	8.89617	+	5.13620i	1.04122	+	0.601147i	0.920178	−	0.391500i	$-0.128044\pi$
$73$	8.89617	+	5.13620i	1.04122	+	0.601147i	0.121040	+	0.992648i	$0.461377\pi$
$74$	−12.6245	−	0.683641i	−1.46757	−	0.0794716i
$75$	2.31912	+	4.01683i	0.267789	+	0.463824i
$76$	−0.201763	+	0.275681i	−0.0231438	+	0.0316228i
$77$		0			0
$78$	4.95378	−	2.51324i	0.560905	−	0.284568i
$79$	12.4661	−	7.19733i	1.40255	−	0.809763i	0.407897	−	0.913028i	$-0.366262\pi$
$79$	12.4661	−	7.19733i	1.40255	−	0.809763i	0.994654	+	0.103265i	$0.0329290\pi$
$80$	−2.66633	+	12.1286i	−0.298105	+	1.35602i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	6.92240	+	4.51259i	0.764451	+	0.498333i
$83$	10.9783			1.20503			0.602515	−	0.798108i	$-0.294165\pi$
$83$	10.9783			1.20503			0.602515	+	0.798108i	$0.294165\pi$
$84$		0			0
$85$	17.6394			1.91326
$86$	2.82300	+	1.84027i	0.304412	+	0.198441i
$87$	0.984084	−	1.70448i	0.105505	−	0.182740i
$88$	11.6981	+	9.57440i	1.24702	+	1.02063i
$89$	−5.03915	+	2.90936i	−0.534149	+	0.308391i	−0.742704	−	0.669619i	$-0.766457\pi$
$89$	−5.03915	+	2.90936i	−0.534149	+	0.308391i	0.208555	+	0.978011i	$0.433124\pi$
$90$	−3.91542	+	1.98644i	−0.412722	+	0.209389i
$91$		0			0
$92$	−9.89588	−	7.24251i	−1.03172	−	0.755084i
$93$	0.765577	+	1.32602i	0.0793867	+	0.137502i
$94$	−3.24055	−	0.175482i	−0.334238	−	0.0180996i
$95$	−0.459251	−	0.265149i	−0.0471182	−	0.0272037i
$96$	−5.45116	−	1.51156i	−0.556357	−	0.154273i
$97$		−	2.32666i		−	0.236237i	−0.993000	−	0.118118i	$-0.962314\pi$
$97$		−	2.32666i		−	0.236237i	0.993000	−	0.118118i	$-0.0376862\pi$
$98$		0			0
$99$			5.34455i			0.537148i
$100$	−9.22222	−	1.00174i	−0.922222	−	0.100174i
$101$	6.44694	+	3.72214i	0.641494	+	0.370367i	0.785190	−	0.619255i	$-0.212565\pi$
$101$	6.44694	+	3.72214i	0.641494	+	0.370367i	−0.143696	+	0.989622i	$0.545899\pi$
$102$	−0.434488	+	8.02350i	−0.0430208	+	0.794445i
$103$	8.14796	+	14.1127i	0.802842	+	1.39056i	0.917738	+	0.397186i	$0.130013\pi$
$103$	8.14796	+	14.1127i	0.802842	+	1.39056i	−0.114896	+	0.993378i	$0.536653\pi$
$104$	−1.79517	+	10.9637i	−0.176031	+	1.07508i
$105$		0			0
$106$	−0.767206	−	1.51222i	−0.0745176	−	0.146880i
$107$	−14.4966	+	8.36959i	−1.40143	+	0.809119i	−0.994540	−	0.104356i	$-0.966722\pi$
$107$	−14.4966	+	8.36959i	−1.40143	+	0.809119i	−0.406895	+	0.913475i	$0.633388\pi$
$108$	−0.807113	−	1.82991i	−0.0776645	−	0.176083i
$109$	−3.86058	+	6.68673i	−0.369777	+	0.640472i	−0.989530	−	0.144324i	$-0.953899\pi$
$109$	−3.86058	+	6.68673i	−0.369777	+	0.640472i	0.619754	+	0.784796i	$0.287233\pi$
$110$	−12.8143	+	19.6573i	−1.22180	+	1.87425i
$111$	8.93993			0.848541
$112$		0			0
$113$	−0.715845			−0.0673410			−0.0336705	−	0.999433i	$-0.510720\pi$
$113$	−0.715845			−0.0673410			−0.0336705	+	0.999433i	$0.510720\pi$
$114$	0.131918	−	0.202365i	0.0123553	−	0.0189532i
$115$	9.51782	−	16.4853i	0.887541	−	1.53727i
$116$	1.58853	+	3.60157i	0.147492	+	0.334397i
$117$	−3.40163	+	1.96393i	−0.314481	+	0.181566i
$118$	7.03462	+	13.8658i	0.647589	+	1.27645i
$119$		0			0
$120$	1.41889	−	8.66560i	0.129526	−	0.791058i
$121$	8.78211	+	15.2111i	0.798374	+	1.38282i
$122$	0.503923	−	9.30571i	0.0456230	−	0.842500i
$123$	−5.06025	−	2.92154i	−0.456268	−	0.263426i
$124$	−3.04440	−	0.330691i	−0.273395	−	0.0296969i
$125$			1.12312i			0.100455i
$126$		0			0
$127$		−	15.4079i		−	1.36723i	−0.729844	−	0.683614i	$-0.760407\pi$
$127$		−	15.4079i		−	1.36723i	0.729844	−	0.683614i	$-0.239593\pi$
$128$	8.87843	−	7.01238i	0.784750	−	0.619812i
$129$	−2.06361	−	1.19142i	−0.181691	−	0.104899i
$130$	−17.2201	−	0.932501i	−1.51030	−	0.0817858i
$131$	−1.12959	−	1.95651i	−0.0986927	−	0.170941i	0.812451	−	0.583029i	$-0.198133\pi$
$131$	−1.12959	−	1.95651i	−0.0986927	−	0.170941i	−0.911144	+	0.412089i	$0.864799\pi$
$132$	−8.62576	−	6.31294i	−0.750776	−	0.549471i
$133$		0			0
$134$	12.1679	−	6.17321i	1.05114	−	0.533284i
$135$	2.68862	−	1.55228i	0.231400	−	0.133599i
$136$	−12.4362	−	10.1785i	−1.06639	−	0.872801i
$137$	−10.0365	+	17.3838i	−0.857479	+	1.48520i	0.0168472	+	0.999858i	$0.494637\pi$
$137$	−10.0365	+	17.3838i	−0.857479	+	1.48520i	−0.874326	+	0.485339i	$0.838696\pi$
$138$	7.26413	+	4.73536i	0.618364	+	0.403101i
$139$	7.98360			0.677160			0.338580	−	0.940938i	$-0.390053\pi$
$139$	7.98360			0.677160			0.338580	+	0.940938i	$0.390053\pi$
$140$		0			0
$141$	2.29477			0.193255
$142$	2.42451	+	1.58050i	0.203460	+	0.132632i
$143$	−10.4963	+	18.1802i	−0.877749	+	1.52031i
$144$	3.90671	+	0.858847i	0.325559	+	0.0715706i
$145$	−5.29165	+	3.05514i	−0.439448	+	0.253715i
$146$	12.9554	−	6.57277i	1.07220	−	0.543966i
$147$		0			0
$148$	−10.5598	+	14.4285i	−0.868008	+	1.18601i
$149$	2.65085	+	4.59141i	0.217166	+	0.376143i	0.953940	−	0.299996i	$-0.0969854\pi$
$149$	2.65085	+	4.59141i	0.217166	+	0.376143i	−0.736774	+	0.676139i	$0.763652\pi$
$150$	6.54986	+	0.354688i	0.534794	+	0.0289601i
$151$	−1.32205	−	0.763288i	−0.107587	−	0.0621155i	0.445241	−	0.895411i	$-0.353118\pi$
$151$	−1.32205	−	0.763288i	−0.107587	−	0.0621155i	−0.552828	+	0.833295i	$0.686451\pi$
$152$	0.170783	+	0.451940i	0.0138524	+	0.0366572i
$153$		−	5.68178i		−	0.459345i
$154$		0			0
$155$		−	4.75355i		−	0.381814i
$156$	0.848320	−	7.80980i	0.0679200	−	0.625284i
$157$	−10.7697	−	6.21791i	−0.859519	−	0.496243i	0.00433223	−	0.999991i	$-0.498621\pi$
$157$	−10.7697	−	6.21791i	−0.859519	−	0.496243i	−0.863851	+	0.503747i	$0.831954\pi$
$158$	1.10077	−	20.3273i	0.0875723	−	1.61716i
$159$	0.599523	+	1.03840i	0.0475453	+	0.0823508i
$160$	12.3097	+	12.5257i	0.973170	+	0.990246i
$161$		0			0
$162$	0.639847	+	1.26119i	0.0502711	+	0.0990883i
$163$	5.38969	−	3.11174i	0.422153	−	0.243730i	−0.273845	−	0.961774i	$-0.588296\pi$
$163$	5.38969	−	3.11174i	0.422153	−	0.243730i	0.695998	+	0.718044i	$0.254962\pi$
$164$	10.6923	−	4.71602i	0.834928	−	0.368259i
$165$	8.29621	−	14.3695i	0.645859	−	1.11866i
$166$	8.47855	−	13.0062i	0.658063	−	1.00948i
$167$	−4.14549			−0.320788			−0.160394	−	0.987053i	$-0.551276\pi$
$167$	−4.14549			−0.320788			−0.160394	+	0.987053i	$0.551276\pi$
$168$		0			0
$169$	−2.42816			−0.186781
$170$	13.6228	−	20.8977i	1.04482	−	1.60278i
$171$	−0.0854065	+	0.147928i	−0.00653120	+	0.0113124i
$172$	4.36040	−	1.92323i	0.332477	−	0.146645i
$173$	−4.80327	+	2.77317i	−0.365186	+	0.210840i	−0.671353	−	0.741137i	$-0.734287\pi$
$173$	−4.80327	+	2.77317i	−0.365186	+	0.210840i	0.306167	+	0.951978i	$0.400953\pi$
$174$	−1.25933	−	2.48223i	−0.0954693	−	0.188177i
$175$		0			0
$176$	20.3773	−	6.46462i	1.53600	−	0.487289i
$177$	−5.49711	−	9.52127i	−0.413188	−	0.715663i
$178$	−0.444960	+	8.21686i	−0.0333511	+	0.615880i
$179$	1.10129	+	0.635830i	0.0823143	+	0.0475242i	0.540592	−	0.841285i	$-0.318200\pi$
$179$	1.10129	+	0.635830i	0.0823143	+	0.0475242i	−0.458278	+	0.888809i	$0.651534\pi$
$180$	−0.670504	+	6.17279i	−0.0499764	+	0.460093i
$181$			0.386679i			0.0287416i	0.999897	+	0.0143708i	$0.00457452\pi$
$181$			0.386679i			0.0287416i	−0.999897	+	0.0143708i	$0.995425\pi$
$182$		0			0
$183$			6.58977i			0.487130i
$184$	−16.2229	+	6.13046i	−1.19597	+	0.451943i
$185$	−24.0361	−	13.8772i	−1.76717	−	1.02028i
$186$	2.16221	+	0.117088i	0.158541	+	0.00858531i
$187$	−15.1833	−	26.2982i	−1.11031	−	1.92312i
$188$	−2.71057	+	3.70362i	−0.197689	+	0.270114i
$189$		0			0
$190$	−0.668805	+	0.339309i	−0.0485202	+	0.0246161i
$191$	5.71184	−	3.29773i	0.413295	−	0.238616i	−0.278910	−	0.960317i	$-0.589973\pi$
$191$	5.71184	−	3.29773i	0.413295	−	0.238616i	0.692204	+	0.721702i	$0.256640\pi$
$192$	−6.00070	+	5.29071i	−0.433063	+	0.381824i
$193$	−0.978531	+	1.69487i	−0.0704362	+	0.121999i	−0.899093	−	0.437759i	$-0.855772\pi$
$193$	−0.978531	+	1.69487i	−0.0704362	+	0.121999i	0.828656	+	0.559758i	$0.189106\pi$
$194$	−2.75644	−	1.79687i	−0.197901	−	0.129008i
$195$	12.1943			0.873250
$196$		0			0
$197$	−0.362935			−0.0258580			−0.0129290	−	0.999916i	$-0.504116\pi$
$197$	−0.362935			−0.0258580			−0.0129290	+	0.999916i	$0.504116\pi$
$198$	6.33178	+	4.12758i	0.449980	+	0.293335i
$199$	4.93167	−	8.54190i	0.349597	−	0.605519i	−0.636581	−	0.771210i	$-0.719652\pi$
$199$	4.93167	−	8.54190i	0.349597	−	0.605519i	0.986178	+	0.165691i	$0.0529853\pi$
$200$	−8.30908	+	10.1521i	−0.587541	+	0.717861i
$201$	−8.35536	+	4.82397i	−0.589342	+	0.340257i
$202$	9.38864	−	4.76320i	0.660583	−	0.335138i
$203$		0			0
$204$	9.17002	+	6.71127i	0.642030	+	0.469883i
$205$	9.07006	+	15.7098i	0.633481	+	1.09722i
$206$	23.0122	+	1.24616i	1.60334	+	0.0868238i
$207$	−5.31006	−	3.06576i	−0.369075	−	0.213085i
$208$	11.6025	+	10.5940i	0.804487	+	0.734562i
$209$			0.912919i			0.0631479i
$210$		0			0
$211$		−	25.7279i		−	1.77118i	−0.464469	−	0.885589i	$-0.653755\pi$
$211$		−	25.7279i		−	1.77118i	0.464469	−	0.885589i	$-0.346245\pi$
$212$	−2.38407	−	0.258964i	−0.163739	−	0.0177857i
$213$	−1.77231	−	1.02324i	−0.121437	−	0.0701114i
$214$	−1.28005	+	23.6381i	−0.0875026	+	1.61587i
$215$	3.69884	+	6.40657i	0.252259	+	0.436925i
$216$	−2.79126	−	0.457034i	−0.189921	−	0.0310972i
$217$		0			0
$218$	4.94037	+	9.73785i	0.334604	+	0.659530i
$219$	−8.89617	+	5.13620i	−0.601147	+	0.347073i
$220$	13.3920	+	30.3626i	0.902886	+	2.04705i
$221$	11.1586	−	19.3273i	0.750612	−	1.30010i
$222$	6.90429	−	10.5913i	0.463386	−	0.710842i
$223$	−16.2449			−1.08784			−0.543919	−	0.839138i	$-0.683060\pi$
$223$	−16.2449			−1.08784			−0.543919	+	0.839138i	$0.683060\pi$
$224$		0			0
$225$	−4.63824			−0.309216
$226$	−0.552845	+	0.848074i	−0.0367747	+	0.0564131i
$227$	10.2242	−	17.7088i	0.678603	−	1.17537i	−0.296799	−	0.954940i	$-0.595919\pi$
$227$	10.2242	−	17.7088i	0.678603	−	1.17537i	0.975402	−	0.220434i	$-0.0707475\pi$
$228$	−0.137865	−	0.312572i	−0.00913036	−	0.0207006i
$229$	2.93541	−	1.69476i	0.193977	−	0.111993i	−0.399866	−	0.916574i	$-0.630943\pi$
$229$	2.93541	−	1.69476i	0.193977	−	0.111993i	0.593843	+	0.804581i	$0.297610\pi$
$230$	−12.1799	−	24.0075i	−0.803118	−	1.58301i
$231$		0			0
$232$	5.49366	+	0.899520i	0.360677	+	0.0590564i
$233$	−0.952184	−	1.64923i	−0.0623796	−	0.108045i	0.833149	−	0.553049i	$-0.186536\pi$
$233$	−0.952184	−	1.64923i	−0.0623796	−	0.108045i	−0.895529	+	0.445004i	$0.853202\pi$
$234$	−0.300366	+	5.54672i	−0.0196355	+	0.362600i
$235$	−6.16978	−	3.56212i	−0.402472	−	0.232367i
$236$	21.8599	+	2.37447i	1.42296	+	0.154565i
$237$			14.3947i			0.935034i
$238$		0			0
$239$			7.77419i			0.502871i	0.967874	+	0.251435i	$0.0809026\pi$
$239$			7.77419i			0.502871i	−0.967874	+	0.251435i	$0.919097\pi$
$240$	−9.17049	−	8.37340i	−0.591953	−	0.540501i
$241$	10.4882	+	6.05535i	0.675603	+	0.390060i	0.798196	−	0.602397i	$-0.205788\pi$
$241$	10.4882	+	6.05535i	0.675603	+	0.390060i	−0.122593	+	0.992457i	$0.539121\pi$
$242$	24.8032	+	1.34314i	1.59441	+	0.0863406i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−10.6355	−	7.78379i	−0.680866	−	0.498306i
$245$		0			0
$246$	−7.36922	+	3.73867i	−0.469844	+	0.238369i
$247$	−0.581043	+	0.335466i	−0.0369709	+	0.0213452i
$248$	−2.74296	+	3.35137i	−0.174178	+	0.212812i
$249$	−5.48917	+	9.50752i	−0.347862	+	0.602515i
$250$	1.33058	+	0.867380i	0.0841530	+	0.0548579i
$251$	−7.89409			−0.498271			−0.249135	−	0.968469i	$-0.580146\pi$
$251$	−7.89409			−0.498271			−0.249135	+	0.968469i	$0.580146\pi$
$252$		0			0
$253$	−32.7703			−2.06025
$254$	−18.2540	−	11.8995i	−1.14536	−	0.746639i
$255$	−8.81969	+	15.2761i	−0.552310	+	0.956630i
$256$	−1.45089	−	15.9341i	−0.0906808	−	0.995880i
$257$	−2.65277	+	1.53158i	−0.165475	+	0.0955372i	−0.580451	−	0.814295i	$-0.697124\pi$
$257$	−2.65277	+	1.53158i	−0.165475	+	0.0955372i	0.414975	+	0.909833i	$0.363790\pi$
$258$	−3.00522	+	1.52466i	−0.187097	+	0.0949211i
$259$		0			0
$260$	−14.4038	+	19.6808i	−0.893284	+	1.22055i
$261$	0.984084	+	1.70448i	0.0609133	+	0.105505i
$262$	−3.19029	−	0.172760i	−0.197097	−	0.0106732i
$263$	9.20446	+	5.31420i	0.567571	+	0.327687i	0.756179	−	0.654365i	$-0.227064\pi$
$263$	9.20446	+	5.31420i	0.567571	+	0.327687i	−0.188607	+	0.982053i	$0.560397\pi$
$264$	−14.1407	+	5.34362i	−0.870300	+	0.328877i
$265$		−	3.72250i		−	0.228671i
$266$		0			0
$267$		−	5.81871i		−	0.356099i
$268$	2.08371	−	19.1830i	0.127283	−	1.17179i
$269$	−2.17816	−	1.25756i	−0.132805	−	0.0766748i	0.432126	−	0.901813i	$-0.357764\pi$
$269$	−2.17816	−	1.25756i	−0.132805	−	0.0766748i	−0.564930	+	0.825139i	$0.691097\pi$
$270$	0.237406	−	4.38407i	0.0144481	−	0.266806i
$271$	0.458106	+	0.793463i	0.0278279	+	0.0481994i	0.879604	−	0.475707i	$-0.157808\pi$
$271$	0.458106	+	0.793463i	0.0278279	+	0.0481994i	−0.851776	+	0.523906i	$0.824474\pi$
$272$	−21.6631	+	6.87252i	−1.31352	+	0.416708i
$273$		0			0
$274$	12.8437	+	25.3159i	0.775916	+	1.52939i
$275$	−21.4682	+	12.3946i	−1.29458	+	0.747425i
$276$	11.2201	−	4.94883i	0.675373	−	0.297885i
$277$	−5.88292	+	10.1895i	−0.353470	+	0.612229i	−0.986855	−	0.161609i	$-0.948332\pi$
$277$	−5.88292	+	10.1895i	−0.353470	+	0.612229i	0.633385	+	0.773837i	$0.281665\pi$
$278$	6.16571	−	9.45831i	0.369795	−	0.567272i
$279$	−1.53115			−0.0916678
$280$		0			0
$281$	−29.8347			−1.77979			−0.889895	−	0.456165i	$-0.849223\pi$
$281$	−29.8347			−1.77979			−0.889895	+	0.456165i	$0.849223\pi$
$282$	1.77225	−	2.71866i	0.105536	−	0.161894i
$283$	−2.41492	+	4.18276i	−0.143552	+	0.248639i	−0.928832	−	0.370502i	$-0.879186\pi$
$283$	−2.41492	+	4.18276i	−0.143552	+	0.248639i	0.785280	+	0.619141i	$0.212519\pi$
$284$	3.74488	−	1.65174i	0.222218	−	0.0980130i
$285$	0.459251	−	0.265149i	0.0272037	−	0.0157061i
$286$	13.4321	+	26.4757i	0.794258	+	1.56554i
$287$		0			0
$288$	4.03463	−	3.96506i	0.237743	−	0.233644i
$289$	7.64132	+	13.2352i	0.449489	+	0.778538i
$290$	−0.467256	+	8.62859i	−0.0274382	+	0.506688i
$291$	2.01495	+	1.16333i	0.118118	+	0.0681956i
$292$	2.21858	−	20.4247i	0.129833	−	1.19526i
$293$		−	22.4276i		−	1.31023i	−0.755528	−	0.655116i	$-0.772620\pi$
$293$		−	22.4276i		−	1.31023i	0.755528	−	0.655116i	$-0.227380\pi$
$294$		0			0
$295$			34.1321i			1.98725i
$296$	8.93838	+	23.6534i	0.519533	+	1.37483i
$297$	−4.62852	−	2.67228i	−0.268574	−	0.155061i
$298$	7.48677	+	0.405423i	0.433697	+	0.0234855i
$299$	−12.0419	−	20.8572i	−0.696402	−	1.20620i
$300$	5.47865	−	7.48581i	0.316310	−	0.432193i
$301$		0			0
$302$	−1.92530	+	0.976774i	−0.110788	+	0.0562071i
$303$	−6.44694	+	3.72214i	−0.370367	+	0.213831i
$304$	0.667317	+	0.146702i	0.0382732	+	0.00841395i
$305$	10.2291	−	17.7174i	0.585719	−	1.01450i
$306$	−6.73131	−	4.38803i	−0.384803	−	0.250847i
$307$	−31.3123			−1.78709			−0.893543	−	0.448978i	$-0.851788\pi$
$307$	−31.3123			−1.78709			−0.893543	+	0.448978i	$0.851788\pi$
$308$		0			0
$309$	−16.2959			−0.927042
$310$	−5.63161	−	3.67115i	−0.319854	−	0.208507i
$311$	7.71105	−	13.3559i	0.437253	−	0.757345i	−0.560223	−	0.828342i	$-0.689285\pi$
$311$	7.71105	−	13.3559i	0.437253	−	0.757345i	0.997477	+	0.0709966i	$0.0226180\pi$
$312$	−8.59725	−	7.03651i	−0.486724	−	0.398364i
$313$	5.28101	−	3.04900i	0.298501	−	0.172339i	−0.343269	−	0.939237i	$-0.611534\pi$
$313$	5.28101	−	3.04900i	0.298501	−	0.172339i	0.641769	+	0.766898i	$0.278201\pi$
$314$	−15.6839	+	7.95703i	−0.885095	+	0.449041i
$315$		0			0
$316$	−23.2320	−	17.0029i	−1.30690	−	0.956485i
$317$	14.8555	+	25.7305i	0.834369	+	1.44517i	0.894543	+	0.446982i	$0.147501\pi$
$317$	14.8555	+	25.7305i	0.834369	+	1.44517i	−0.0601742	+	0.998188i	$0.519166\pi$
$318$	1.69323	+	0.0916916i	0.0949514	+	0.00514181i
$319$	9.10970	+	5.25949i	0.510045	+	0.294475i
$320$	24.3462	−	4.90998i	1.36100	−	0.274476i
$321$		−	16.7392i		−	0.934290i
$322$		0			0
$323$		−	0.970522i		−	0.0540013i
$324$	1.98830	+	0.215975i	0.110461	+	0.0119986i
$325$	−15.7776	−	9.10919i	−0.875183	−	0.505287i
$326$	0.475912	−	8.78845i	0.0263583	−	0.486747i
$327$	−3.86058	−	6.68673i	−0.213491	−	0.369777i
$328$	2.67048	−	16.3095i	0.147453	−	0.900543i
$329$		0			0
$330$	−10.6166	−	20.9262i	−0.584425	−	1.15195i
$331$	−17.4697	+	10.0861i	−0.960220	+	0.554383i	−0.896241	−	0.443568i	$-0.853712\pi$
$331$	−17.4697	+	10.0861i	−0.960220	+	0.554383i	−0.0639792	+	0.997951i	$0.520379\pi$
$332$	−8.86076	−	20.0894i	−0.486297	−	1.10255i
$333$	−4.46997	+	7.74221i	−0.244953	+	0.424271i
$334$	−3.20155	+	4.91123i	−0.175181	+	0.268731i
$335$	29.9525			1.63648
$336$		0			0
$337$	14.0021			0.762746			0.381373	−	0.924421i	$-0.375451\pi$
$337$	14.0021			0.762746			0.381373	+	0.924421i	$0.375451\pi$
$338$	−1.87526	+	2.87668i	−0.102001	+	0.156471i
$339$	0.357923	−	0.619940i	0.0194397	−	0.0336705i
$340$	−14.2370	−	32.2785i	−0.772108	−	1.75055i
$341$	−7.08697	+	4.09167i	−0.383781	+	0.221576i
$342$	0.109294	+	0.215427i	0.00590995	+	0.0116490i
$343$		0			0
$344$	1.08904	−	6.65115i	0.0587173	−	0.358606i
$345$	9.51782	+	16.4853i	0.512422	+	0.887541i
$346$	−0.424131	+	7.83224i	−0.0228014	+	0.421064i
$347$	−10.3801	−	5.99294i	−0.557231	−	0.321718i	0.194802	−	0.980843i	$-0.437594\pi$
$347$	−10.3801	−	5.99294i	−0.557231	−	0.321718i	−0.752034	+	0.659125i	$0.770927\pi$
$348$	−3.91332	−	0.425074i	−0.209776	−	0.0227864i
$349$		−	28.8227i		−	1.54284i	−0.636324	−	0.771422i	$-0.719546\pi$
$349$		−	28.8227i		−	1.54284i	0.636324	−	0.771422i	$-0.280454\pi$
$350$		0			0
$351$		−	3.92787i		−	0.209654i
$352$	8.07863	−	29.1340i	0.430592	−	1.55285i
$353$	−0.0994062	−	0.0573922i	−0.00529086	−	0.00305468i	0.497352	−	0.867549i	$-0.334306\pi$
$353$	−0.0994062	−	0.0573922i	−0.00529086	−	0.00305468i	−0.502643	+	0.864494i	$0.667639\pi$
$354$	−15.5254	−	0.840733i	−0.825167	−	0.0446844i
$355$	3.17671	+	5.50222i	0.168602	+	0.292028i
$356$	9.39102	+	6.87301i	0.497723	+	0.364269i
$357$		0			0
$358$	1.60380	−	0.813668i	0.0847636	−	0.0430037i
$359$	1.71229	−	0.988594i	0.0903714	−	0.0521760i	−0.454133	−	0.890934i	$-0.650051\pi$
$359$	1.71229	−	0.988594i	0.0903714	−	0.0521760i	0.544505	+	0.838758i	$0.316718\pi$
$360$	6.79519	+	5.56159i	0.358138	+	0.293122i
$361$	9.48541	−	16.4292i	0.499232	−	0.864696i
$362$	0.458105	+	0.298631i	0.0240775	+	0.0156957i
$363$	−17.5642			−0.921883
$364$		0			0
$365$	31.8912			1.66926
$366$	7.80702	+	5.08927i	0.408080	+	0.266020i
$367$	−13.3895	+	23.1912i	−0.698925	+	1.21057i	0.269915	+	0.962884i	$0.413004\pi$
$367$	−13.3895	+	23.1912i	−0.698925	+	1.21057i	−0.968840	+	0.247689i	$0.920329\pi$
$368$	−5.26604	+	23.9541i	−0.274511	+	1.24869i
$369$	5.06025	−	2.92154i	0.263426	−	0.152089i
$370$	−35.0036	+	17.7586i	−1.81975	+	0.923227i
$371$		0			0
$372$	1.80859	−	2.47118i	0.0937709	−	0.128125i
$373$	−11.5198	−	19.9529i	−0.596474	−	1.03312i	−0.993337	−	0.115245i	$-0.963235\pi$
$373$	−11.5198	−	19.9529i	−0.596474	−	1.03312i	0.396863	−	0.917878i	$-0.370099\pi$
$374$	−42.8820	−	2.32215i	−2.21737	−	0.120075i
$375$	−0.972647	−	0.561558i	−0.0502273	−	0.0289987i
$376$	2.29438	+	6.07155i	0.118323	+	0.313117i
$377$			7.73071i			0.398152i
$378$		0			0
$379$		−	22.3697i		−	1.14906i	−0.818485	−	0.574528i	$-0.805186\pi$
$379$		−	22.3697i		−	1.14906i	0.818485	−	0.574528i	$-0.194814\pi$
$380$	−0.114531	+	1.05439i	−0.00587531	+	0.0540892i
$381$	13.3436	+	7.70394i	0.683614	+	0.394685i
$382$	0.504358	−	9.31376i	0.0258052	−	0.476533i
$383$	14.3541	+	24.8621i	0.733463	+	1.27039i	0.955395	+	0.295332i	$0.0954304\pi$
$383$	14.3541	+	24.8621i	0.733463	+	1.27039i	−0.221932	+	0.975062i	$0.571236\pi$
$384$	1.63368	+	11.1951i	0.0833683	+	0.571299i
$385$		0			0
$386$	1.25222	+	2.46822i	0.0637363	+	0.125629i
$387$	2.06361	−	1.19142i	0.104899	−	0.0605635i
$388$	−4.25758	+	1.87788i	−0.216146	+	0.0953348i
$389$	−6.17469	+	10.6949i	−0.313069	+	0.542252i	−0.979025	−	0.203739i	$-0.934690\pi$
$389$	−6.17469	+	10.6949i	−0.313069	+	0.542252i	0.665956	+	0.745991i	$0.268024\pi$
$390$	9.41761	−	14.4468i	0.476879	−	0.731541i
$391$	34.8380			1.76183
$392$		0			0
$393$	2.25918			0.113961
$394$	−0.280294	+	0.429976i	−0.0141210	+	0.0216619i
$395$	22.3445	−	38.7018i	1.12427	−	1.94730i
$396$	9.78005	−	4.31366i	0.491466	−	0.216769i
$397$	−15.5877	+	8.99955i	−0.782323	+	0.451674i	−0.837253	−	0.546816i	$-0.815840\pi$
$397$	−15.5877	+	8.99955i	−0.782323	+	0.451674i	0.0549300	+	0.998490i	$0.482506\pi$
$398$	−6.31102	−	12.4395i	−0.316343	−	0.623537i
$399$		0			0
$400$	5.61028	+	17.6844i	0.280514	+	0.884218i
$401$	0.0284861	+	0.0493394i	0.00142253	+	0.00246389i	0.866736	−	0.498768i	$-0.166214\pi$
$401$	0.0284861	+	0.0493394i	0.00142253	+	0.00246389i	−0.865313	+	0.501231i	$0.832881\pi$
$402$	−0.737782	+	13.6243i	−0.0367972	+	0.679518i
$403$	−5.20843	−	3.00709i	−0.259450	−	0.149794i
$404$	1.60778	−	14.8015i	0.0799899	−	0.736402i
$405$			3.10455i			0.154266i
$406$		0			0
$407$			47.7799i			2.36836i
$408$	15.0330	−	5.68079i	0.744242	−	0.281241i
$409$	30.3303	+	17.5112i	1.49974	+	0.865873i	1.00000		0.000305480i	$-9.72372e-5\pi$
$409$	30.3303	+	17.5112i	1.49974	+	0.865873i	0.499735	+	0.866178i	$0.333431\pi$
$410$	25.6165	+	1.38718i	1.26511	+	0.0685081i
$411$	−10.0365	−	17.3838i	−0.495066	−	0.857479i
$412$	19.2486	−	26.3005i	0.948311	−	1.29574i
$413$		0			0
$414$	−7.73301	+	3.92324i	−0.380057	+	0.192817i
$415$	29.5166	−	17.0414i	1.44891	−	0.836530i
$416$	21.5115	−	5.56394i	1.05469	−	0.272795i
$417$	−3.99180	+	6.91400i	−0.195479	+	0.338580i
$418$	1.08155	+	0.705045i	0.0529004	+	0.0344849i
$419$	17.9222			0.875558			0.437779	−	0.899083i	$-0.355765\pi$
$419$	17.9222			0.875558			0.437779	+	0.899083i	$0.355765\pi$
$420$		0			0
$421$	−8.47542			−0.413067			−0.206533	−	0.978440i	$-0.566218\pi$
$421$	−8.47542			−0.413067			−0.206533	+	0.978440i	$0.566218\pi$
$422$	−30.4802	−	19.8696i	−1.48376	−	0.967235i
$423$	−1.14739	+	1.98733i	−0.0557879	+	0.0966275i
$424$	−2.14801	+	2.62445i	−0.104317	+	0.127455i
$425$	22.8227	−	13.1767i	1.10707	−	0.639165i
$426$	−2.58100	+	1.30944i	−0.125050	+	0.0634424i
$427$		0			0
$428$	27.0159	+	19.7722i	1.30587	+	0.955725i
$429$	−10.4963	−	18.1802i	−0.506769	−	0.877749i
$430$	10.4466	+	0.565704i	0.503779	+	0.0272806i
$431$	−20.7836	−	11.9994i	−1.00111	−	0.577990i	−0.0925326	−	0.995710i	$-0.529496\pi$
$431$	−20.7836	−	11.9994i	−1.00111	−	0.577990i	−0.908576	+	0.417719i	$0.862830\pi$
$432$	−2.69714	+	2.95389i	−0.129766	+	0.142119i
$433$			12.5505i			0.603137i	0.953445	+	0.301568i	$0.0975102\pi$
$433$			12.5505i			0.603137i	−0.953445	+	0.301568i	$0.902490\pi$
$434$		0			0
$435$		−	6.11028i		−	0.292965i
$436$	15.3520	+	1.66758i	0.735229	+	0.0798624i
$437$	−0.907027	−	0.523672i	−0.0433890	−	0.0250506i
$438$	−0.785536	+	14.5061i	−0.0375343	+	0.693130i
$439$	−3.57575	−	6.19338i	−0.170661	−	0.295594i	0.767990	−	0.640462i	$-0.221257\pi$
$439$	−3.57575	−	6.19338i	−0.170661	−	0.295594i	−0.938651	+	0.344868i	$0.887924\pi$
$440$	46.3137	+	7.58330i	2.20792	+	0.361520i
$441$		0			0
$442$	−14.2797	−	28.1463i	−0.679214	−	1.33878i
$443$	21.5400	−	12.4361i	1.02340	−	0.590858i	0.108310	−	0.994117i	$-0.465456\pi$
$443$	21.5400	−	12.4361i	1.02340	−	0.590858i	0.915086	+	0.403259i	$0.132123\pi$
$444$	−7.21554	−	16.3593i	−0.342434	−	0.776377i
$445$	−9.03224	+	15.6443i	−0.428169	+	0.741611i
$446$	−12.5459	+	19.2456i	−0.594065	+	0.911306i
$447$	−5.30170			−0.250762
$448$		0			0
$449$	−9.93727			−0.468969			−0.234484	−	0.972120i	$-0.575340\pi$
$449$	−9.93727			−0.468969			−0.234484	+	0.972120i	$0.575340\pi$
$450$	−3.58210	+	5.49500i	−0.168862	+	0.259037i
$451$	15.6143	−	27.0448i	0.735249	−	1.27349i
$452$	0.577768	+	1.30993i	0.0271759	+	0.0616140i
$453$	1.32205	−	0.763288i	0.0621155	−	0.0358624i
$454$	−13.0838	−	25.7892i	−0.614054	−	1.21035i
$455$		0			0
$456$	−0.476783	−	0.0780674i	−0.0223274	−	0.00365584i
$457$	−13.0455	−	22.5955i	−0.610245	−	1.05698i	−0.991199	−	0.132381i	$-0.957738\pi$
$457$	−13.0455	−	22.5955i	−0.610245	−	1.05698i	0.380954	−	0.924594i	$-0.375596\pi$
$458$	0.259198	−	4.78649i	0.0121115	−	0.223658i
$459$	4.92057	+	2.84089i	0.229672	+	0.132601i
$460$	−37.8486	−	4.11121i	−1.76470	−	0.191686i
$461$			29.5120i			1.37451i	0.726417	+	0.687254i	$0.241184\pi$
$461$			29.5120i			1.37451i	−0.726417	+	0.687254i	$0.758816\pi$
$462$		0			0
$463$		−	2.80479i		−	0.130350i	−0.997874	−	0.0651748i	$-0.979239\pi$
$463$		−	2.80479i		−	0.130350i	0.997874	−	0.0651748i	$-0.0207605\pi$
$464$	5.30842	−	5.81374i	0.246437	−	0.269896i
$465$	4.11669	+	2.37677i	0.190907	+	0.110220i
$466$	−2.68924	−	0.145628i	−0.124577	−	0.00674608i
$467$	16.4855	+	28.5537i	0.762857	+	1.32131i	0.941372	+	0.337370i	$0.109537\pi$
$467$	16.4855	+	28.5537i	0.762857	+	1.32131i	−0.178515	+	0.983937i	$0.557129\pi$
$468$	6.33933	+	4.63957i	0.293035	+	0.214464i
$469$		0			0
$470$	−8.98501	+	4.55843i	−0.414448	+	0.210265i
$471$	10.7697	−	6.21791i	0.496243	−	0.286506i
$472$	19.6954	−	24.0640i	0.906554	−	1.10763i
$473$	6.36763	−	11.0291i	0.292784	−	0.507117i
$474$	17.0536	+	11.1170i	0.783298	+	0.510619i
$475$	−0.792271			−0.0363519
$476$		0			0
$477$	−1.19905			−0.0549006
$478$	9.21022	+	6.00399i	0.421266	+	0.274616i
$479$	−11.9626	+	20.7198i	−0.546585	+	0.946713i	0.451920	+	0.892058i	$0.350739\pi$
$479$	−11.9626	+	20.7198i	−0.546585	+	0.946713i	−0.998505	+	0.0546549i	$0.982594\pi$
$480$	−17.0025	+	4.39769i	−0.776053	+	0.200726i
$481$	−30.4104	+	17.5574i	−1.38659	+	0.800551i
$482$	15.2739	−	7.74900i	0.695706	−	0.352957i
$483$		0			0
$484$	20.7467	−	28.3475i	0.943033	−	1.28852i
$485$	−3.61162	−	6.25550i	−0.163995	−	0.284048i
$486$	−1.41214	−	0.0764704i	−0.0640562	−	0.00346877i
$487$	−0.712047	−	0.411101i	−0.0322659	−	0.0186287i	0.483780	−	0.875189i	$-0.339263\pi$
$487$	−0.712047	−	0.411101i	−0.0322659	−	0.0186287i	−0.516046	+	0.856561i	$0.672597\pi$
$488$	−17.4353	+	6.58863i	−0.789261	+	0.298253i
$489$			6.22348i			0.281435i
$490$		0			0
$491$		−	22.6377i		−	1.02163i	−0.859692	−	0.510813i	$-0.829345\pi$
$491$		−	22.6377i		−	1.02163i	0.859692	−	0.510813i	$-0.170655\pi$
$492$	−1.26196	+	11.6178i	−0.0568934	+	0.523771i
$493$	−9.68450	−	5.59135i	−0.436168	−	0.251822i
$494$	−0.0513064	+	0.947452i	−0.00230838	+	0.0426279i
$495$	8.29621	+	14.3695i	0.372887	+	0.645859i
$496$	1.85204	+	5.83788i	0.0831591	+	0.262129i
$497$		0			0
$498$	7.02446	+	13.8458i	0.314774	+	0.620443i
$499$	−25.9699	+	14.9937i	−1.16257	+	0.671211i	−0.951919	−	0.306350i	$-0.900892\pi$
$499$	−25.9699	+	14.9937i	−1.16257	+	0.671211i	−0.210652	+	0.977561i	$0.567559\pi$
$500$	2.05520	−	0.906482i	0.0919114	−	0.0405391i
$501$	2.07274	−	3.59010i	0.0926034	−	0.160394i
$502$	−6.09659	+	9.35227i	−0.272104	+	0.417412i
$503$	−28.7539			−1.28207			−0.641037	−	0.767510i	$-0.721496\pi$
$503$	−28.7539			−1.28207			−0.641037	+	0.767510i	$0.721496\pi$
$504$		0			0
$505$	23.1112			1.02843
$506$	−25.3084	+	38.8235i	−1.12510	+	1.72592i
$507$	1.21408	−	2.10285i	0.0539191	−	0.0933907i
$508$	−28.1950	+	12.4359i	−1.25095	+	0.551754i
$509$	35.5470	−	20.5230i	1.57559	−	0.909668i	0.580128	−	0.814526i	$-0.303003\pi$
$509$	35.5470	−	20.5230i	1.57559	−	0.909668i	0.995464	−	0.0951425i	$-0.0303307\pi$
$510$	11.2865	+	22.2466i	0.499775	+	0.985095i
$511$		0			0
$512$	−19.9979	−	10.5870i	−0.883791	−	0.467882i
$513$	−0.0854065	−	0.147928i	−0.00377079	−	0.00653120i
$514$	−0.234241	+	4.32562i	−0.0103319	+	0.190795i
$515$	43.8135	+	25.2958i	1.93065	+	1.11466i
$516$	−0.514635	+	4.73783i	−0.0226555	+	0.208571i
$517$			12.2645i			0.539394i
$518$		0			0
$519$		−	5.54634i		−	0.243457i
$520$	12.1921	+	32.2638i	0.534661	+	1.41486i
$521$	−17.6887	−	10.2126i	−0.774955	−	0.447420i	0.0596846	−	0.998217i	$-0.480991\pi$
$521$	−17.6887	−	10.2126i	−0.774955	−	0.447420i	−0.834639	+	0.550797i	$0.814324\pi$
$522$	2.77934	+	0.150507i	0.121648	+	0.00658750i
$523$	0.953706	+	1.65187i	0.0417026	+	0.0722311i	0.886123	−	0.463449i	$-0.153388\pi$
$523$	0.953706	+	1.65187i	0.0417026	+	0.0722311i	−0.844421	+	0.535681i	$0.820055\pi$
$524$	−2.66852	+	3.64617i	−0.116575	+	0.159284i
$525$		0			0
$526$	13.4044	−	6.80055i	0.584460	−	0.296518i
$527$	7.53415	−	4.34984i	0.328193	−	0.189482i
$528$	−4.59015	+	20.8796i	−0.199761	+	0.908668i
$529$	7.29781	−	12.6402i	0.317296	−	0.549573i
$530$	−4.41011	−	2.87488i	−0.191563	−	0.124877i
$531$	10.9942			0.477108
$532$		0			0
$533$	22.9508			0.994111
$534$	−6.89353	−	4.49378i	−0.298312	−	0.194465i
$535$	−25.9838	+	45.0053i	−1.12338	+	1.94575i
$536$	−21.1173	−	17.2836i	−0.912126	−	0.746539i
$537$	−1.10129	+	0.635830i	−0.0475242	+	0.0274381i
$538$	−3.17204	+	1.60929i	−0.136756	+	0.0693815i
$539$		0			0
$540$	−5.01054	−	3.66707i	−0.215619	−	0.157806i
$541$	−17.7612	−	30.7633i	−0.763614	−	1.32262i	−0.940976	−	0.338472i	$-0.890090\pi$
$541$	−17.7612	−	30.7633i	−0.763614	−	1.32262i	0.177363	−	0.984146i	$-0.443243\pi$
$542$	1.29382	+	0.0700631i	0.0555745	+	0.00300947i
$543$	−0.334873	−	0.193339i	−0.0143708	−	0.00829698i
$544$	−8.58837	+	30.9723i	−0.368223	+	1.32793i
$545$			23.9708i			1.02679i
$546$		0			0
$547$		−	9.02584i		−	0.385917i	−0.981207	−	0.192959i	$-0.938192\pi$
$547$		−	9.02584i		−	0.385917i	0.981207	−	0.192959i	$-0.0618083\pi$
$548$	39.9114	+	4.33527i	1.70493	+	0.185194i
$549$	−5.70691	−	3.29489i	−0.243565	−	0.140622i
$550$	−1.89565	+	35.0061i	−0.0808307	+	1.49266i
$551$	0.168094	+	0.291148i	0.00716106	+	0.0124033i
$552$	2.80232	−	17.1147i	0.119274	−	0.728449i
$553$		0			0
$554$	7.52833	+	14.8389i	0.319848	+	0.630446i
$555$	24.0361	−	13.8772i	1.02028	−	0.589056i
$556$	−6.44366	−	14.6093i	−0.273272	−	0.619571i
$557$	−16.9960	+	29.4380i	−0.720145	+	1.24733i	0.240796	+	0.970576i	$0.422591\pi$
$557$	−16.9960	+	29.4380i	−0.720145	+	1.24733i	−0.960941	+	0.276752i	$0.910742\pi$
$558$	−1.18251	+	1.81399i	−0.0500595	+	0.0767922i
$559$	9.35952			0.395865
$560$		0			0
$561$	30.3666			1.28208
$562$	−23.0413	+	35.3457i	−0.971938	+	1.49097i
$563$	−6.41295	+	11.1076i	−0.270274	+	0.468128i	−0.968932	−	0.247328i	$-0.920447\pi$
$563$	−6.41295	+	11.1076i	−0.270274	+	0.468128i	0.698658	+	0.715456i	$0.253781\pi$
$564$	−1.85214	−	4.19923i	−0.0779892	−	0.176820i
$565$	−1.92464	+	1.11119i	−0.0809700	+	0.0467481i
$566$	3.09036	+	6.09133i	0.129897	+	0.256038i
$567$		0			0
$568$	0.935313	−	5.71227i	0.0392449	−	0.239681i
$569$	−8.84882	−	15.3266i	−0.370962	−	0.642525i	0.618752	−	0.785586i	$-0.287639\pi$
$569$	−8.84882	−	15.3266i	−0.370962	−	0.642525i	−0.989714	+	0.143062i	$0.954305\pi$
$570$	0.0405521	−	0.748857i	0.00169854	−	0.0313662i
$571$	−20.5992	−	11.8930i	−0.862050	−	0.497705i	0.00264805	−	0.999996i	$-0.499157\pi$
$571$	−20.5992	−	11.8930i	−0.862050	−	0.497705i	−0.864698	+	0.502292i	$0.832490\pi$
$572$	41.7399	+	4.53389i	1.74523	+	0.189572i
$573$			6.59547i			0.275530i
$574$		0			0
$575$		−	28.4395i		−	1.18601i
$576$	−1.58154	−	7.84211i	−0.0658976	−	0.326755i
$577$	−35.1145	−	20.2734i	−1.46184	−	0.843991i	−0.462740	−	0.886494i	$-0.653134\pi$
$577$	−35.1145	−	20.2734i	−1.46184	−	0.843991i	−0.999096	+	0.0425027i	$0.986467\pi$
$578$	21.5813	+	1.16867i	0.897663	+	0.0486103i
$579$	−0.978531	−	1.69487i	−0.0406664	−	0.0704362i
$580$	9.86159	+	7.21741i	0.409480	+	0.299687i
$581$		0			0
$582$	2.93436	−	1.48871i	0.121633	−	0.0617089i
$583$	−5.54981	+	3.20418i	−0.229849	+	0.132704i
$584$	−22.4841	−	18.4023i	−0.930398	−	0.761493i
$585$	−6.09713	+	10.5605i	−0.252086	+	0.436625i
$586$	−26.5703	−	17.3207i	−1.09761	−	0.715513i
$587$	−26.0331			−1.07450			−0.537251	−	0.843422i	$-0.680537\pi$
$587$	−26.0331			−1.07450			−0.537251	+	0.843422i	$0.680537\pi$
$588$		0			0
$589$	−0.261541			−0.0107766
$590$	40.4369	+	26.3601i	1.66476	+	1.08523i
$591$	0.181467	−	0.314311i	0.00746457	−	0.0129290i
$592$	34.9257	+	7.67803i	1.43544	+	0.315565i
$593$	−9.71614	+	5.60962i	−0.398994	+	0.230359i	−0.686050	−	0.727555i	$-0.740657\pi$
$593$	−9.71614	+	5.60962i	−0.398994	+	0.230359i	0.287056	+	0.957914i	$0.407323\pi$
$594$	−6.74049	+	3.41969i	−0.276565	+	0.140312i
$595$		0			0
$596$	6.26232	−	8.55660i	0.256515	−	0.350492i
$597$	4.93167	+	8.54190i	0.201840	+	0.349597i
$598$	−34.0099	−	1.84170i	−1.39077	−	0.0753128i
$599$	15.0686	+	8.69988i	0.615688	+	0.355467i	0.775188	−	0.631730i	$-0.217655\pi$
$599$	15.0686	+	8.69988i	0.615688	+	0.355467i	−0.159501	+	0.987198i	$0.550988\pi$
$600$	−4.63743	−	12.2719i	−0.189322	−	0.500999i
$601$			18.1962i			0.742237i	0.928585	+	0.371119i	$0.121026\pi$
$601$			18.1962i			0.742237i	−0.928585	+	0.371119i	$0.878974\pi$
$602$		0			0
$603$		−	9.64794i		−	0.392895i
$604$	−0.329702	+	3.03530i	−0.0134154	+	0.123504i
$605$	47.2235	+	27.2645i	1.91991	+	1.10846i
$606$	−0.569268	+	10.5124i	−0.0231249	+	0.427037i
$607$	2.72854	+	4.72597i	0.110748	+	0.191821i	0.916072	−	0.401014i	$-0.131342\pi$
$607$	2.72854	+	4.72597i	0.110748	+	0.191821i	−0.805324	+	0.592835i	$0.798009\pi$
$608$	0.689168	−	0.677284i	0.0279495	−	0.0274675i
$609$		0			0
$610$	−13.0902	−	25.8018i	−0.530006	−	1.04468i
$611$	−7.80599	+	4.50679i	−0.315796	+	0.182325i
$612$	−10.3971	+	4.58584i	−0.420280	+	0.185372i
$613$	15.0526	−	26.0718i	0.607967	−	1.05303i	−0.383608	−	0.923496i	$-0.625319\pi$
$613$	15.0526	−	26.0718i	0.607967	−	1.05303i	0.991575	−	0.129534i	$-0.0413480\pi$
$614$	−24.1824	+	37.0962i	−0.975922	+	1.49708i
$615$	−18.1401			−0.731480
$616$		0			0
$617$	38.4324			1.54723			0.773616	−	0.633655i	$-0.218446\pi$
$617$	38.4324			1.54723			0.773616	+	0.633655i	$0.218446\pi$
$618$	−12.5853	+	19.3061i	−0.506255	+	0.776604i
$619$	−9.16780	+	15.8791i	−0.368485	+	0.638235i	−0.989329	−	0.145700i	$-0.953457\pi$
$619$	−9.16780	+	15.8791i	−0.368485	+	0.638235i	0.620844	+	0.783934i	$0.286790\pi$
$620$	−8.69856	+	3.83665i	−0.349343	+	0.154084i
$621$	5.31006	−	3.06576i	0.213085	−	0.123025i
$622$	−9.86778	−	19.4502i	−0.395662	−	0.779881i
$623$		0			0
$624$	−14.9759	+	4.75104i	−0.599517	+	0.190194i
$625$	13.3390	+	23.1038i	0.533559	+	0.924151i
$626$	0.466316	−	8.61124i	0.0186377	−	0.344175i
$627$	−0.790611	−	0.456459i	−0.0315740	−	0.0182292i
$628$	−2.68582	+	24.7262i	−0.107176	+	0.986683i
$629$		−	50.7948i		−	2.02532i
$630$		0			0
$631$			44.4442i			1.76930i	0.466259	+	0.884648i	$0.345601\pi$
$631$			44.4442i			1.76930i	−0.466259	+	0.884648i	$0.654399\pi$
$632$	−38.0856	+	14.3922i	−1.51497	+	0.572489i
$633$	22.2810	+	12.8639i	0.885589	+	0.511295i
$634$	41.9563	+	2.27202i	1.66630	+	0.0902333i
$635$	−23.9173	−	41.4259i	−0.949128	−	1.64394i
$636$	1.41630	−	1.93518i	0.0561601	−	0.0767350i
$637$		0			0
$638$	13.2664	−	6.73053i	0.525222	−	0.266464i
$639$	1.77231	−	1.02324i	0.0701114	−	0.0404789i
$640$	12.9856	−	32.6354i	0.513301	−	1.29003i
$641$	−0.413761	+	0.716656i	−0.0163426	+	0.0283062i	−0.874081	−	0.485780i	$-0.838536\pi$
$641$	−0.413761	+	0.716656i	−0.0163426	+	0.0283062i	0.857738	+	0.514086i	$0.171869\pi$
$642$	−19.8312	−	12.9276i	−0.782675	−	0.510213i
$643$	50.0469			1.97366			0.986829	−	0.161764i	$-0.0517183\pi$
$643$	50.0469			1.97366			0.986829	+	0.161764i	$0.0517183\pi$
$644$		0			0
$645$	−7.39767			−0.291283
$646$	−1.14979	−	0.749532i	−0.0452381	−	0.0294899i
$647$	−8.66100	+	15.0013i	−0.340499	+	0.589761i	−0.984525	−	0.175242i	$-0.943929\pi$
$647$	−8.66100	+	15.0013i	−0.340499	+	0.589761i	0.644026	+	0.765003i	$0.277263\pi$
$648$	1.79143	−	2.18878i	0.0703741	−	0.0859835i
$649$	50.8869	−	29.3796i	1.99749	−	1.15325i
$650$	−22.9768	+	11.6570i	−0.901225	+	0.457224i
$651$		0			0
$652$	−10.0443	−	7.35112i	−0.393365	−	0.287892i
$653$	−3.48003	−	6.02759i	−0.136184	−	0.235878i	0.789865	−	0.613281i	$-0.210151\pi$
$653$	−3.48003	−	6.02759i	−0.136184	−	0.235878i	−0.926049	+	0.377403i	$0.876817\pi$
$654$	−10.9034	−	0.590441i	−0.426357	−	0.0230881i
$655$	−6.07407	−	3.50687i	−0.237334	−	0.137025i
$656$	−17.2598	−	15.7596i	−0.673881	−	0.615308i
$657$		−	10.2724i		−	0.400765i
$658$		0			0
$659$		−	20.5979i		−	0.802381i	−0.915995	−	0.401191i	$-0.868596\pi$
$659$		−	20.5979i		−	0.802381i	0.915995	−	0.401191i	$-0.131404\pi$
$660$	−32.9908	−	3.58354i	−1.28417	−	0.139489i
$661$	37.8931	+	21.8776i	1.47387	+	0.850940i	0.999567	−	0.0294204i	$-0.00936616\pi$
$661$	37.8931	+	21.8776i	1.47387	+	0.850940i	0.474305	+	0.880361i	$0.342699\pi$
$662$	−1.54258	+	28.4861i	−0.0599541	+	1.10714i
$663$	11.1586	+	19.3273i	0.433366	+	0.750612i
$664$	−30.6434	−	5.01748i	−1.18919	−	0.194716i
$665$		0			0
$666$	5.72019	+	11.2749i	0.221653	+	0.436895i
$667$	−10.4511	+	6.03394i	−0.404668	+	0.233635i
$668$	3.34588	+	7.58587i	0.129456	+	0.293506i
$669$	8.12244	−	14.0685i	0.314032	−	0.543919i
$670$	23.1323	−	35.4853i	0.893677	−	1.37092i
$671$	−35.2194			−1.35963
$672$		0			0
$673$	5.42765			0.209220			0.104610	−	0.994513i	$-0.466641\pi$
$673$	5.42765			0.209220			0.104610	+	0.994513i	$0.466641\pi$
$674$	10.8138	−	16.5886i	0.416533	−	0.638969i
$675$	2.31912	−	4.01683i	0.0892629	−	0.154608i
$676$	1.95980	+	4.44331i	0.0753768	+	0.170897i
$677$	−29.3631	+	16.9528i	−1.12852	+	0.651549i	−0.943561	−	0.331198i	$-0.892547\pi$
$677$	−29.3631	+	16.9528i	−1.12852	+	0.651549i	−0.184955	+	0.982747i	$0.559214\pi$
$678$	−0.458031	−	0.902815i	−0.0175906	−	0.0346724i
$679$		0			0
$680$	−49.2361	−	8.06180i	−1.88812	−	0.309156i
$681$	10.2242	+	17.7088i	0.391791	+	0.678603i
$682$	−0.625783	+	11.5561i	−0.0239625	+	0.442504i
$683$	−5.10771	−	2.94894i	−0.195441	−	0.112838i	0.399086	−	0.916913i	$-0.369327\pi$
$683$	−5.10771	−	2.94894i	−0.195441	−	0.112838i	−0.594527	+	0.804076i	$0.702661\pi$
$684$	0.339628	+	0.0368913i	0.0129860	+	0.00141057i
$685$			62.3179i			2.38104i
$686$		0			0
$687$			3.38952i			0.129318i
$688$	−7.03867	−	6.42687i	−0.268347	−	0.245022i
$689$	−4.07872	−	2.35485i	−0.155387	−	0.0897126i
$690$	26.8811	+	1.45566i	1.02334	+	0.0554162i
$691$	21.6635	+	37.5223i	0.824119	+	1.42742i	0.902590	+	0.430500i	$0.141663\pi$
$691$	21.6635	+	37.5223i	0.824119	+	1.42742i	−0.0784711	+	0.996916i	$0.525004\pi$
$692$	8.95144	+	6.55129i	0.340283	+	0.249043i
$693$		0			0
$694$	−15.1164	+	7.66913i	−0.573812	+	0.291116i
$695$	21.4649	−	12.3927i	0.814209	−	0.470084i
$696$	−3.52584	+	4.30789i	−0.133647	+	0.163290i
$697$	−16.5995	+	28.7512i	−0.628752	+	1.08903i
$698$	−34.1468	−	22.2597i	−1.29247	−	0.842543i
$699$	1.90437			0.0720298
$700$		0			0
$701$	28.9345			1.09284			0.546420	−	0.837511i	$-0.315990\pi$
$701$	28.9345			1.09284			0.546420	+	0.837511i	$0.315990\pi$
$702$	−4.65342	−	3.03348i	−0.175632	−	0.114491i
$703$	−0.763529	+	1.32247i	−0.0287970	+	0.0498779i
$704$	−28.2765	−	32.0710i	−1.06571	−	1.20872i
$705$	6.16978	−	3.56212i	0.232367	−	0.134157i
$706$	−0.144765	+	0.0734444i	−0.00544829	+	0.00276412i
$707$		0			0
$708$	−12.9863	+	17.7440i	−0.488054	+	0.666859i
$709$	−8.37917	−	14.5131i	−0.314686	−	0.545053i	0.664684	−	0.747124i	$-0.268566\pi$
$709$	−8.37917	−	14.5131i	−0.314686	−	0.545053i	−0.979371	+	0.202072i	$0.935233\pi$
$710$	8.97194	+	0.485849i	0.336711	+	0.0182336i
$711$	−12.4661	−	7.19733i	−0.467517	−	0.269921i
$712$	15.3952	−	5.81770i	0.576961	−	0.218027i
$713$		−	9.38831i		−	0.351595i
$714$		0			0
$715$			65.1729i			2.43733i
$716$	0.274646	−	2.52845i	0.0102640	−	0.0944925i
$717$	−6.73265	−	3.88710i	−0.251435	−	0.145166i
$718$	0.151196	−	2.79207i	0.00564260	−	0.104199i
$719$	15.4119	+	26.6943i	0.574768	+	0.995528i	0.996067	+	0.0886057i	$0.0282411\pi$
$719$	15.4119	+	26.6943i	0.574768	+	0.995528i	−0.421299	+	0.906922i	$0.638426\pi$
$720$	11.8368	−	3.75518i	0.441132	−	0.139947i
$721$		0			0
$722$	−12.1384	−	23.9258i	−0.451745	−	0.890425i
$723$	−10.4882	+	6.05535i	−0.390060	+	0.225201i
$724$	0.707587	−	0.312093i	0.0262973	−	0.0115989i
$725$	−4.56441	+	7.90579i	−0.169518	+	0.293614i
$726$	−13.5648	+	20.8087i	−0.503437	+	0.772281i
$727$	20.6890			0.767313			0.383657	−	0.923476i	$-0.374665\pi$
$727$	20.6890			0.767313			0.383657	+	0.923476i	$0.374665\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	24.6295	−	37.7821i	0.911579	−	1.39838i
$731$	−6.76941	+	11.7250i	−0.250376	+	0.433664i
$732$	12.0587	−	5.31869i	0.445702	−	0.196584i
$733$	21.8336	−	12.6057i	0.806444	−	0.465601i	−0.0392754	−	0.999228i	$-0.512505\pi$
$733$	21.8336	−	12.6057i	0.806444	−	0.465601i	0.845719	+	0.533628i	$0.179172\pi$
$734$	17.1344	+	33.7733i	0.632443	+	1.24660i
$735$		0			0
$736$	24.3119	+	24.7385i	0.896148	+	0.911872i
$737$	−25.7820	−	44.6557i	−0.949691	−	1.64491i
$738$	0.446823	−	8.25127i	0.0164478	−	0.303733i
$739$	25.2048	+	14.5520i	0.927175	+	0.535305i	0.885917	−	0.463844i	$-0.153530\pi$
$739$	25.2048	+	14.5520i	0.927175	+	0.535305i	0.0412579	+	0.999149i	$0.486863\pi$
$740$	−5.99426	+	55.1844i	−0.220354	+	2.02862i
$741$		−	0.670931i		−	0.0246473i
$742$		0			0
$743$			4.72777i			0.173445i	0.996233	+	0.0867226i	$0.0276394\pi$
$743$			4.72777i			0.173445i	−0.996233	+	0.0867226i	$0.972361\pi$
$744$	−1.53089	−	4.05115i	−0.0561251	−	0.148523i
$745$	14.2543	+	8.22970i	0.522235	+	0.301513i
$746$	−32.5353	−	1.76185i	−1.19120	−	0.0645060i
$747$	−5.48917	−	9.50752i	−0.200838	−	0.347862i
$748$	−35.8687	+	49.0097i	−1.31149	+	1.79197i
$749$		0			0
$750$	−1.41646	+	0.718623i	−0.0517219	+	0.0262404i
$751$	6.37092	−	3.67825i	0.232478	−	0.134221i	−0.379237	−	0.925300i	$-0.623813\pi$
$751$	6.37092	−	3.67825i	0.232478	−	0.134221i	0.611715	+	0.791078i	$0.290480\pi$
$752$	8.96502	+	1.97086i	0.326921	+	0.0718699i
$753$	3.94704	−	6.83648i	0.143838	−	0.249135i
$754$	9.15871	+	5.97041i	0.333540	+	0.217429i
$755$	−4.73933			−0.172482
$756$		0			0
$757$	6.36602			0.231377			0.115688	−	0.993286i	$-0.463093\pi$
$757$	6.36602			0.231377			0.115688	+	0.993286i	$0.463093\pi$
$758$	−26.5018	−	17.2761i	−0.962590	−	0.627496i
$759$	16.3851	−	28.3799i	0.594742	−	1.03012i
$760$	1.16071	+	0.949992i	0.0421033	+	0.0344598i
$761$	1.74679	−	1.00851i	0.0633210	−	0.0365584i	−0.468005	−	0.883726i	$-0.655027\pi$
$761$	1.74679	−	1.00851i	0.0633210	−	0.0365584i	0.531326	+	0.847167i	$0.321694\pi$
$762$	19.4322	−	9.85868i	0.703956	−	0.357142i
$763$		0			0
$764$	−10.6447	−	7.79051i	−0.385110	−	0.281851i
$765$	−8.81969	−	15.2761i	−0.318877	−	0.552310i
$766$	40.5403	+	2.19534i	1.46478	+	0.0793207i
$767$	37.3983	+	21.5919i	1.35037	+	0.779639i
$768$	14.5248	+	6.71053i	0.524117	+	0.242145i
$769$		−	52.1122i		−	1.87922i	−0.342253	−	0.939608i	$-0.611190\pi$
$769$		−	52.1122i		−	1.87922i	0.342253	−	0.939608i	$-0.388810\pi$
$770$		0			0
$771$		−	3.06316i		−	0.110317i
$772$	3.89124	+	0.422676i	0.140049	+	0.0152124i
$773$	21.8398	+	12.6092i	0.785524	+	0.453523i	0.838385	−	0.545079i	$-0.183500\pi$
$773$	21.8398	+	12.6092i	0.785524	+	0.453523i	−0.0528601	+	0.998602i	$0.516834\pi$
$774$	0.182218	−	3.36493i	0.00654967	−	0.120950i
$775$	−3.55093	−	6.15039i	−0.127553	−	0.220928i
$776$	−1.06336	+	6.49431i	−0.0381725	+	0.233132i
$777$		0			0
$778$	7.90171	+	15.5749i	0.283290	+	0.558387i
$779$	0.864357	−	0.499037i	0.0309688	−	0.0178798i
$780$	−9.84215	−	22.3144i	−0.352406	−	0.798984i
$781$	5.46877	−	9.47219i	0.195688	−	0.338942i
$782$	26.9053	−	41.2732i	0.962132	−	1.47593i
$783$	−1.96817			−0.0703366
$784$		0			0
$785$	−38.6077			−1.37797
$786$	1.74476	−	2.67649i	0.0622335	−	0.0954672i
$787$	−11.7425	+	20.3386i	−0.418574	+	0.724992i	−0.995796	−	0.0915954i	$-0.970803\pi$
$787$	−11.7425	+	20.3386i	−0.418574	+	0.724992i	0.577222	+	0.816587i	$0.304137\pi$
$788$	0.292929	+	0.664138i	0.0104352	+	0.0236589i
$789$	−9.20446	+	5.31420i	−0.327687	+	0.189190i
$790$	−28.5941	−	56.3612i	−1.01733	−	2.00524i
$791$		0			0
$792$	2.44264	−	14.9180i	0.0867955	−	0.530089i
$793$	−12.9419	−	22.4160i	−0.459580	−	0.796016i
$794$	−1.37640	+	25.4173i	−0.0488466	+	0.902027i
$795$	3.22378	+	1.86125i	0.114336	+	0.0660117i
$796$	−19.6113	−	2.13023i	−0.695104	−	0.0755040i
$797$		−	44.2469i		−	1.56730i	−0.621200	−	0.783652i	$-0.713354\pi$
$797$		−	44.2469i		−	1.56730i	0.621200	−	0.783652i	$-0.286646\pi$
$798$		0			0
$799$		−	13.0384i		−	0.461266i
$800$	25.2838	+	7.01099i	0.893916	+	0.247876i
$801$	5.03915	+	2.90936i	0.178050	+	0.102797i
$802$	0.0804531	+	0.00435670i	0.00284090	+	0.000153840i
$803$	−27.4507	−	47.5460i	−0.968714	−	1.67786i
$804$	15.5712	+	11.3961i	0.549152	+	0.401908i
$805$		0			0
$806$	−7.58501	+	3.84815i	−0.267170	+	0.135545i
$807$	2.17816	−	1.25756i	0.0766748	−	0.0442682i
$808$	−16.2939	−	13.3359i	−0.573218	−	0.469156i
$809$	14.9871	−	25.9585i	0.526920	−	0.912652i	−0.472588	−	0.881284i	$-0.656680\pi$
$809$	14.9871	−	25.9585i	0.526920	−	0.912652i	0.999508	−	0.0313688i	$-0.00998663\pi$
$810$	3.67802	+	2.39764i	0.129232	+	0.0842444i
$811$	8.74124			0.306946			0.153473	−	0.988153i	$-0.450954\pi$
$811$	8.74124			0.306946			0.153473	+	0.988153i	$0.450954\pi$
$812$		0			0
$813$	−0.916212			−0.0321329
$814$	56.6057	+	36.9003i	1.98403	+	1.29336i
$815$	9.66055	−	16.7326i	0.338394	−	0.586116i
$816$	4.87978	−	22.1971i	0.170826	−	0.777053i
$817$	0.352491	−	0.203511i	0.0123321	−	0.00711994i
$818$	44.1698	−	22.4090i	1.54436	−	0.783511i
$819$		0			0
$820$	21.4270	−	29.2770i	0.748262	−	1.02240i
$821$	24.0064	+	41.5802i	0.837828	+	1.45116i	0.891707	+	0.452613i	$0.149508\pi$
$821$	24.0064	+	41.5802i	0.837828	+	1.45116i	−0.0538792	+	0.998547i	$0.517159\pi$
$822$	−28.3461	−	1.53500i	−0.988683	−	0.0535391i
$823$	−17.4328	−	10.0648i	−0.607669	−	0.350838i	0.164384	−	0.986396i	$-0.447436\pi$
$823$	−17.4328	−	10.0648i	−0.607669	−	0.350838i	−0.772053	+	0.635559i	$0.780770\pi$
$824$	−16.2931	−	43.1160i	−0.567596	−	1.50202i
$825$		−	24.7893i		−	0.863052i
$826$		0			0
$827$			24.4464i			0.850084i	0.905174	+	0.425042i	$0.139741\pi$
$827$			24.4464i			0.850084i	−0.905174	+	0.425042i	$0.860259\pi$
$828$	−1.32425	+	12.1913i	−0.0460210	+	0.423678i
$829$	−9.36761	−	5.40839i	−0.325350	−	0.187841i	0.328425	−	0.944530i	$-0.393482\pi$
$829$	−9.36761	−	5.40839i	−0.325350	−	0.187841i	−0.653775	+	0.756689i	$0.726816\pi$
$830$	2.60633	−	48.1299i	0.0904670	−	1.67061i
$831$	−5.88292	−	10.1895i	−0.204076	−	0.353470i
$832$	10.0216	−	29.7820i	0.347435	−	1.03251i
$833$		0			0
$834$	5.10828	+	10.0688i	0.176885	+	0.348655i
$835$	−11.1456	+	6.43494i	−0.385711	+	0.222690i
$836$	1.67056	−	0.736828i	0.0577775	−	0.0254837i
$837$	0.765577	−	1.32602i	0.0264622	−	0.0458339i
$838$	13.8413	−	21.2328i	0.478139	−	0.733474i
$839$	−10.6831			−0.368821			−0.184410	−	0.982849i	$-0.559038\pi$
$839$	−10.6831			−0.368821			−0.184410	+	0.982849i	$0.559038\pi$
$840$		0			0
$841$	−25.1263			−0.866425
$842$	−6.54555	+	10.0410i	−0.225574	+	0.346035i
$843$	14.9174	−	25.8376i	0.513781	−	0.889895i
$844$	−47.0796	+	20.7653i	−1.62055	+	0.714770i
$845$	−6.52839	+	3.76917i	−0.224584	+	0.129663i
$846$	1.46830	+	2.89414i	0.0504814	+	0.0995027i
$847$		0			0
$848$	1.45033	+	4.57164i	0.0498046	+	0.156991i
$849$	−2.41492	−	4.18276i	−0.0828798	−	0.143552i
$850$	2.01526	−	37.2149i	0.0691228	−	1.27646i
$851$	−47.4716	−	27.4077i	−1.62730	−	0.939525i
$852$	−0.441989	+	4.06904i	−0.0151423	+	0.139403i
$853$			47.6336i			1.63094i	0.578796	+	0.815472i	$0.303523\pi$
$853$			47.6336i			1.63094i	−0.578796	+	0.815472i	$0.696477\pi$
$854$		0			0
$855$			0.530298i			0.0181358i
$856$	44.2888	−	16.7363i	1.51376	−	0.572034i
$857$	−15.5236	−	8.96257i	−0.530277	−	0.306156i	0.210852	−	0.977518i	$-0.432376\pi$
$857$	−15.5236	−	8.96257i	−0.530277	−	0.306156i	−0.741129	+	0.671362i	$0.765709\pi$
$858$	−29.6447	−	1.60532i	−1.01205	−	0.0548048i
$859$	−9.63082	−	16.6811i	−0.328599	−	0.569151i	0.653635	−	0.756810i	$-0.273243\pi$
$859$	−9.63082	−	16.6811i	−0.328599	−	0.569151i	−0.982234	+	0.187659i	$0.939910\pi$
$860$	8.73807	−	11.9394i	0.297966	−	0.407129i
$861$		0			0
$862$	−30.2670	+	15.3555i	−1.03090	+	0.523012i
$863$	6.55647	−	3.78538i	0.223185	−	0.128856i	−0.384239	−	0.923234i	$-0.625536\pi$
$863$	6.55647	−	3.78538i	0.223185	−	0.128856i	0.607424	+	0.794378i	$0.292203\pi$
$864$	1.41653	+	5.47663i	0.0481913	+	0.186319i
$865$	−8.60945	+	14.9120i	−0.292730	+	0.507023i
$866$	14.8688	+	9.69270i	0.505261	+	0.329371i
$867$	−15.2826			−0.519026
$868$		0			0
$869$	−76.9330			−2.60977
$870$	−7.23895	−	4.71895i	−0.245424	−	0.159987i
$871$	18.9479	−	32.8188i	0.642026	−	1.11202i
$872$	13.8319	−	16.9000i	0.468409	−	0.572305i
$873$	−2.01495	+	1.16333i	−0.0681956	+	0.0393728i
$874$	−1.32090	+	0.670140i	−0.0446801	+	0.0226678i
$875$		0			0
$876$	16.5790	+	12.1337i	0.560152	+	0.409959i
$877$	11.5486	+	20.0028i	0.389969	+	0.675447i	0.992445	−	0.122690i	$-0.0391522\pi$
$877$	11.5486	+	20.0028i	0.389969	+	0.675447i	−0.602476	+	0.798137i	$0.705819\pi$
$878$	−10.0990	−	0.546879i	−0.340823	−	0.0184563i
$879$	19.4228	+	11.2138i	0.655116	+	0.378231i
$880$	44.7521	−	49.0122i	1.50859	−	1.65220i
$881$			26.0108i			0.876325i	0.898896	+	0.438163i	$0.144371\pi$
$881$			26.0108i			0.876325i	−0.898896	+	0.438163i	$0.855629\pi$
$882$		0			0
$883$		−	13.5662i		−	0.456539i	−0.973598	−	0.228270i	$-0.926693\pi$
$883$		−	13.5662i		−	0.456539i	0.973598	−	0.228270i	$-0.0733068\pi$
$884$	−44.3736	−	4.81997i	−1.49244	−	0.162113i
$885$	−29.5593	−	17.0661i	−0.993624	−	0.573669i
$886$	1.90199	−	35.1232i	0.0638987	−	1.17999i
$887$	−0.579489	−	1.00370i	−0.0194573	−	0.0337011i	0.856133	−	0.516756i	$-0.172861\pi$
$887$	−0.579489	−	1.00370i	−0.0194573	−	0.0337011i	−0.875590	+	0.483055i	$0.839527\pi$
$888$	−24.9537	−	4.08585i	−0.837390	−	0.137112i
$889$		0			0
$890$	11.5585	+	22.7827i	0.387442	+	0.763678i
$891$	4.62852	−	2.67228i	0.155061	−	0.0895246i
$892$	13.1115	+	29.7267i	0.439004	+	0.995323i
$893$	−0.195989	+	0.339462i	−0.00655851	+	0.0113597i
$894$	−4.09449	+	6.28102i	−0.136940	+	0.210069i
$895$	3.94793			0.131965
$896$		0			0
$897$	24.0838			0.804136
$898$	−7.67453	+	11.7729i	−0.256102	+	0.392866i
$899$	−1.50678	+	2.60983i	−0.0502541	+	0.0870426i
$900$	3.74358	+	8.48755i	0.124786	+	0.282918i
$901$	5.89999	−	3.40636i	0.196557	−	0.113482i
$902$	−19.9815	−	39.3852i	−0.665312	−	1.31138i
$903$		0			0
$904$	1.99811	+	0.327166i	0.0664561	+	0.0108814i
$905$	0.600232	+	1.03963i	0.0199524	+	0.0345585i
$906$	0.116738	−	2.15574i	0.00387836	−	0.0716198i
$907$	−32.1580	−	18.5664i	−1.06779	−	0.616488i	−0.140212	−	0.990122i	$-0.544778\pi$
$907$	−32.1580	−	18.5664i	−1.06779	−	0.616488i	−0.927576	+	0.373634i	$0.878112\pi$
$908$	−40.6576	−	4.41633i	−1.34927	−	0.146561i
$909$		−	7.44428i		−	0.246911i
$910$		0			0
$911$		−	27.9490i		−	0.925992i	−0.886360	−	0.462996i	$-0.846774\pi$
$911$		−	27.9490i		−	0.925992i	0.886360	−	0.462996i	$-0.153226\pi$
$912$	−0.460706	+	0.504562i	−0.0152555	+	0.0167077i
$913$	−50.8134	−	29.3372i	−1.68168	−	0.970918i
$914$	−36.8444	−	1.99520i	−1.21870	−	0.0659953i
$915$	10.2291	+	17.7174i	0.338165	+	0.585719i
$916$	−5.47046	−	4.00367i	−0.180749	−	0.132285i
$917$		0			0
$918$	7.16580	−	3.63547i	0.236507	−	0.119988i
$919$	7.46598	−	4.31048i	0.246280	−	0.142190i	−0.371780	−	0.928321i	$-0.621252\pi$
$919$	7.46598	−	4.31048i	0.246280	−	0.142190i	0.618060	+	0.786131i	$0.287919\pi$
$920$	−34.1010	+	41.6649i	−1.12428	+	1.37365i
$921$	15.6561	−	27.1172i	0.515887	−	0.893543i
$922$	34.9633	+	22.7920i	1.15146	+	0.750615i
$923$	8.03833			0.264585
$924$		0			0
$925$	−41.4655			−1.36338
$926$	−3.32288	−	2.16613i	−0.109197	−	0.0711835i
$927$	8.14796	−	14.1127i	0.267614	−	0.463521i
$928$	−2.78797	−	10.7789i	−0.0915195	−	0.353835i
$929$	19.6937	−	11.3702i	0.646129	−	0.373043i	−0.140842	−	0.990032i	$-0.544981\pi$
$929$	19.6937	−	11.3702i	0.646129	−	0.373043i	0.786972	+	0.616989i	$0.211648\pi$
$930$	5.99512	−	3.04154i	0.196588	−	0.0997361i
$931$		0			0
$932$	−2.24942	+	3.07353i	−0.0736823	+	0.100677i
$933$	7.71105	+	13.3559i	0.252448	+	0.437253i
$934$	46.5598	+	2.52130i	1.52348	+	0.0824996i
$935$	−81.6442	−	47.1373i	−2.67005	−	1.54155i
$936$	10.3924	−	3.92719i	0.339687	−	0.128364i
$937$			0.364981i			0.0119234i	0.999982	+	0.00596171i	$0.00189768\pi$
$937$			0.364981i			0.0119234i	−0.999982	+	0.00596171i	$0.998102\pi$
$938$		0			0
$939$			6.09799i			0.199000i
$940$	−1.53866	+	14.1652i	−0.0501854	+	0.462017i
$941$	16.2639	+	9.38995i	0.530187	+	0.306104i	0.741093	−	0.671403i	$-0.234308\pi$
$941$	16.2639	+	9.38995i	0.530187	+	0.306104i	−0.210906	+	0.977506i	$0.567641\pi$
$942$	0.950973	−	17.5612i	0.0309844	−	0.572174i
$943$	17.9135	+	31.0271i	0.583343	+	1.01038i
$944$	−13.2983	−	41.9180i	−0.432823	−	1.36432i
$945$		0			0
$946$	−8.14861	−	16.0616i	−0.264934	−	0.522206i
$947$	3.63927	−	2.10113i	0.118260	−	0.0682776i	−0.439703	−	0.898143i	$-0.644916\pi$
$947$	3.63927	−	2.10113i	0.118260	−	0.0682776i	0.557963	+	0.829866i	$0.311583\pi$
$948$	26.3409	−	11.6181i	0.855514	−	0.377339i
$949$	20.1743	−	34.9430i	0.654887	−	1.13430i
$950$	−0.611869	+	0.938618i	−0.0198517	+	0.0304528i
$951$	−29.7110			−0.963446
$952$		0			0
$953$	−24.9457			−0.808072			−0.404036	−	0.914743i	$-0.632393\pi$
$953$	−24.9457			−0.808072			−0.404036	+	0.914743i	$0.632393\pi$
$954$	−0.926021	+	1.42053i	−0.0299810	+	0.0459914i
$955$	10.2380	−	17.7327i	0.331293	−	0.573817i
$956$	14.2261	−	6.27465i	0.460104	−	0.202937i
$957$	−9.10970	+	5.25949i	−0.294475	+	0.170015i
$958$	15.3085	+	30.1742i	0.494594	+	0.974884i
$959$		0			0
$960$	−7.92095	+	23.5394i	−0.255648	+	0.759732i
$961$	14.3278	+	24.8164i	0.462187	+	0.800531i
$962$	−2.68525	+	49.5873i	−0.0865760	+	1.59876i
$963$	14.4966	+	8.36959i	0.467145	+	0.269706i
$964$	2.61561	−	24.0798i	0.0842430	−	0.775557i
$965$			6.07580i			0.195587i
$966$		0			0
$967$			45.6476i			1.46793i	0.679188	+	0.733964i	$0.262332\pi$
$967$			45.6476i			1.46793i	−0.679188	+	0.733964i	$0.737668\pi$
$968$	−17.5612	−	46.4717i	−0.564437	−	1.49366i
$969$	0.840497	+	0.485261i	0.0270006	+	0.0155888i
$970$	−10.2003	−	0.552364i	−0.327510	−	0.0177353i
$971$	25.3427	+	43.8949i	0.813286	+	1.40865i	0.910552	+	0.413395i	$0.135657\pi$
$971$	25.3427	+	43.8949i	0.813286	+	1.40865i	−0.0972657	+	0.995258i	$0.531010\pi$
$972$	−1.18119	+	1.61393i	−0.0378867	+	0.0517670i
$973$		0			0
$974$	−1.03695	+	0.526083i	−0.0332260	+	0.0168568i
$975$	15.7776	−	9.10919i	0.505287	−	0.291728i
$976$	−5.65961	+	25.7443i	−0.181160	+	0.824056i
$977$	−15.3448	+	26.5780i	−0.490925	+	0.850307i	−0.999945	−	0.0104476i	$-0.996674\pi$
$977$	−15.3448	+	26.5780i	−0.490925	+	0.850307i	0.509021	+	0.860754i	$0.330008\pi$
$978$	7.37306	+	4.80638i	0.235765	+	0.153691i
$979$	31.0984			0.993909
$980$		0			0
$981$	7.72117			0.246518
$982$	−26.8193	−	17.4831i	−0.855838	−	0.557907i
$983$	12.3475	−	21.3864i	0.393823	−	0.682122i	−0.599127	−	0.800654i	$-0.704486\pi$
$983$	12.3475	−	21.3864i	0.393823	−	0.682122i	0.992950	+	0.118532i	$0.0378189\pi$
$984$	12.7892	+	10.4675i	0.407706	+	0.333691i
$985$	−0.975794	+	0.563375i	−0.0310914	+	0.0179506i
$986$	−14.1035	+	7.15522i	−0.449147	+	0.227868i
$987$		0			0
$988$	1.08284	+	0.792498i	0.0344497	+	0.0252127i
$989$	7.30525	+	12.6531i	0.232293	+	0.402344i
$990$	23.4309	+	1.26883i	0.744683	+	0.0403261i
$991$	51.0606	+	29.4799i	1.62199	+	0.936459i	0.986386	+	0.164447i	$0.0525839\pi$
$991$	51.0606	+	29.4799i	1.62199	+	0.936459i	0.635608	+	0.772012i	$0.280749\pi$
$992$	8.34657	+	2.31444i	0.265004	+	0.0734835i
$993$		−	20.1722i		−	0.640147i
$994$		0			0
$995$		−	30.6212i		−	0.970758i
$996$	21.8283	+	2.37104i	0.691656	+	0.0751294i
$997$	−22.2217	−	12.8297i	−0.703767	−	0.406320i	0.104982	−	0.994474i	$-0.466522\pi$
$997$	−22.2217	−	12.8297i	−0.703767	−	0.406320i	−0.808749	+	0.588154i	$0.799855\pi$
$998$	−2.29315	+	42.3466i	−0.0725885	+	1.34046i
$999$	−4.46997	−	7.74221i	−0.141424	−	0.244953i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.2.o.e.31.9		24
4.3	odd	2		588.2.o.f.31.1		24
7.2	even	3	inner	588.2.o.e.19.1		24
7.3	odd	6		588.2.b.c.391.8	yes	12
7.4	even	3		588.2.b.d.391.8	yes	12
7.5	odd	6		588.2.o.f.19.1		24
7.6	odd	2		588.2.o.f.31.9		24
21.11	odd	6		1764.2.b.m.1567.5		12
21.17	even	6		1764.2.b.l.1567.5		12
28.3	even	6		588.2.b.d.391.7	yes	12
28.11	odd	6		588.2.b.c.391.7	✓	12
28.19	even	6	inner	588.2.o.e.19.9		24
28.23	odd	6		588.2.o.f.19.9		24
28.27	even	2	inner	588.2.o.e.31.1		24
84.11	even	6		1764.2.b.l.1567.6		12
84.59	odd	6		1764.2.b.m.1567.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
588.2.b.c.391.7	✓	12	28.11	odd	6
588.2.b.c.391.8	yes	12	7.3	odd	6
588.2.b.d.391.7	yes	12	28.3	even	6
588.2.b.d.391.8	yes	12	7.4	even	3
588.2.o.e.19.1		24	7.2	even	3	inner
588.2.o.e.19.9		24	28.19	even	6	inner
588.2.o.e.31.1		24	28.27	even	2	inner
588.2.o.e.31.9		24	1.1	even	1	trivial
588.2.o.f.19.1		24	7.5	odd	6
588.2.o.f.19.9		24	28.23	odd	6
588.2.o.f.31.1		24	4.3	odd	2
588.2.o.f.31.9		24	7.6	odd	2
1764.2.b.l.1567.5		12	21.17	even	6
1764.2.b.l.1567.6		12	84.11	even	6
1764.2.b.m.1567.5		12	21.11	odd	6
1764.2.b.m.1567.6		12	84.59	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	588.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.772298 - 1.18472i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.807113 - 1.82991i) q^{4} +(2.68862 - 1.55228i) q^{5} +(0.639847 + 1.26119i) q^{6} +(-2.79126 - 0.457034i) q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.237406 - 4.38407i) q^{10} +(-4.62852 - 2.67228i) q^{11} +(1.98830 + 0.215975i) q^{12} -3.92787i q^{13} +3.10455i q^{15} +(-2.69714 + 2.95389i) q^{16} +(4.92057 + 2.84089i) q^{17} +(-1.41214 - 0.0764704i) q^{18} +(-0.0854065 - 0.147928i) q^{19} +(-5.01054 - 3.66707i) q^{20} +(-6.74049 + 3.41969i) q^{22} +(5.31006 - 3.06576i) q^{23} +(1.79143 - 2.18878i) q^{24} +(2.31912 - 4.01683i) q^{25} +(-4.65342 - 3.03348i) q^{26} +1.00000 q^{27} -1.96817 q^{29} +(3.67802 + 2.39764i) q^{30} +(0.765577 - 1.32602i) q^{31} +(1.41653 + 5.47663i) q^{32} +(4.62852 - 2.67228i) q^{33} +(7.16580 - 3.63547i) q^{34} +(-1.18119 + 1.61393i) q^{36} +(-4.46997 - 7.74221i) q^{37} +(-0.241213 - 0.0130621i) q^{38} +(3.40163 + 1.96393i) q^{39} +(-8.21407 + 3.10401i) q^{40} +5.84308i q^{41} +2.38285i q^{43} +(-1.15429 + 10.6266i) q^{44} +(-2.68862 - 1.55228i) q^{45} +(0.468881 - 8.65860i) q^{46} +(-1.14739 - 1.98733i) q^{47} +(-1.20957 - 3.81273i) q^{48} +(-2.96776 - 5.84969i) q^{50} +(-4.92057 + 2.84089i) q^{51} +(-7.18765 + 3.17023i) q^{52} +(0.599523 - 1.03840i) q^{53} +(0.772298 - 1.18472i) q^{54} -16.5924 q^{55} +0.170813 q^{57} +(-1.52001 + 2.33172i) q^{58} +(-5.49711 + 9.52127i) q^{59} +(5.68105 - 2.50572i) q^{60} +(5.70691 - 3.29489i) q^{61} +(-0.979705 - 1.93107i) q^{62} +(7.58224 + 2.55140i) q^{64} +(-6.09713 - 10.5605i) q^{65} +(0.408700 - 7.54728i) q^{66} +(8.35536 + 4.82397i) q^{67} +(1.22712 - 11.2971i) q^{68} +6.13153i q^{69} +2.04649i q^{71} +(0.999826 + 2.64582i) q^{72} +(8.89617 + 5.13620i) q^{73} +(-12.6245 - 0.683641i) q^{74} +(2.31912 + 4.01683i) q^{75} +(-0.201763 + 0.275681i) q^{76} +(4.95378 - 2.51324i) q^{78} +(12.4661 - 7.19733i) q^{79} +(-2.66633 + 12.1286i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(6.92240 + 4.51259i) q^{82} +10.9783 q^{83} +17.6394 q^{85} +(2.82300 + 1.84027i) q^{86} +(0.984084 - 1.70448i) q^{87} +(11.6981 + 9.57440i) q^{88} +(-5.03915 + 2.90936i) q^{89} +(-3.91542 + 1.98644i) q^{90} +(-9.89588 - 7.24251i) q^{92} +(0.765577 + 1.32602i) q^{93} +(-3.24055 - 0.175482i) q^{94} +(-0.459251 - 0.265149i) q^{95} +(-5.45116 - 1.51156i) q^{96} -2.32666i q^{97} +5.34455i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{2} - 12 q^{3} + 4 q^{4} + 8 q^{6} + 8 q^{8} - 12 q^{9} + 4 q^{12} + 4 q^{16} - 4 q^{18} - 48 q^{20} - 4 q^{24} + 12 q^{25} - 24 q^{26} + 24 q^{27} + 64 q^{29} - 16 q^{31} - 4 q^{32} + 64 q^{34}+ \cdots - 4 q^{96}+O(q^{100}) \) 24 * q - 4 * q^2 - 12 * q^3 + 4 * q^4 + 8 * q^6 + 8 * q^8 - 12 * q^9 + 4 * q^12 + 4 * q^16 - 4 * q^18 - 48 * q^20 - 4 * q^24 + 12 * q^25 - 24 * q^26 + 24 * q^27 + 64 * q^29 - 16 * q^31 - 4 * q^32 + 64 * q^34 - 8 * q^36 - 32 * q^37 + 24 * q^38 + 32 * q^40 + 24 * q^44 - 24 * q^46 - 8 * q^48 - 56 * q^50 - 32 * q^52 + 32 * q^53 - 4 * q^54 + 32 * q^55 - 16 * q^58 + 16 * q^59 + 24 * q^60 + 16 * q^62 - 8 * q^64 + 8 * q^68 - 4 * q^72 + 32 * q^74 + 12 * q^75 - 64 * q^76 + 48 * q^78 + 16 * q^80 - 12 * q^81 - 32 * q^82 - 32 * q^83 + 32 * q^85 + 24 * q^86 - 32 * q^87 - 24 * q^88 - 16 * q^93 - 4 * q^96

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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